Quote from al-Muwatta' and its authenticity
Al-Muwatta' is an authentic book narrated via around 100 people, of which around 10 copies of the different narrations (riwayyat) are still available.
As for the report of Sa'id ibn al-Mussayib it is disconnected in al-Muwatta' since imam Malik didn't name the person who told that he heard Sa'id ibn al-Mussayib's reporting about the athar of 'Umar ibn al-Khattab. Nevertheless, ibn 'Abd al-Barr stated in al-Istidhkaar:
لا أعلم الثقة هاهنا من هو ؟ والخبر عن عمر مستفيض من رواية أهل المدينة ، وأهل العراق ، إلا أنها مختلفة المعنى : فمنهم من يروي عن عمر أنه لم يورث الحملاء حملة لا ببينة ، ولا بغير بينة .(Source)
I do not know who is the "reliable source" here. The narration on the authority of Omar is extensive in the narrations of the people of Medina and the people of Iraq, except that their meaning is different: some of them narrate on the authority of Omar that he did not bequeath any inheritance to the bearers, neither with evidence nor without evidence.
This means that this report is well-known and it can be regarded as authentic.
Note that in the version of Muhammad ibn al-Hassan a_Shaybani he mentioned the "reliable source" and named him Bukayr ibn 'Abdullah ibn al-Ashajj بكير بن عبد الله بن الأشج, which would connect the above narration (see here).
here the full text as quoted in sunnah.com:
Yahya related to me from Malik from a reliable source of his who had heard Said ibn al-Musayyab say, ''Umar ibn al-Khattab refused to let anyone inherit from the non-Arabs except for one who was born among the Arabs."
This is an athar of 'Umar ibn al-Khattab.
Malik said, "If a pregnant woman comes from the land of the enemy and gives birth in arab land so that he is her (an arab) child, he inherits from her if she dies, and she inherits from him if he dies, by the Book of Allah."
This is a fatwa statement of imam Malik on the topic. Followed by other statements/fatwas of imam Malik that were recorded by hs students:
Malik said, "The generally agreed-on way of doing things among us and the sunna in which there is no dispute, and what I saw the people of knowledge in our city doing, is that a Muslim does not inherit from a kafir by kinship, clientage (wala'), or maternal relationship, nor does he (the Muslim) overshadow any (of the kafirs) from his inheritance.
Malik said, "Similarly, someone who forgoes his inheritance when he is the chief heir does not overshadow anyone from his inheritance."
Bukayr ibn 'Abdullah al-Ashajj
also known as abu 'Abdullah. He died according to some sources 122 a.H., others said it was 127 a.H. (ibn Manjawayh said he died in Medina) also 117a.H. and 120 a.H. were quoted as al-Bukhari reported. He is counted among the young tabi'i's and lived in Medina and Egypt. He is considered as trustworthy among his students was al-Laith ibn Sa'ad and among his teachers were Sa'id ibn al-Musayyib (according to ibn Manajwayh) and Nafi'i of ibn 'Umar. Al-'Ijli claimed that Malik never heard him since he left to Egypt very early, while al-Bukhari quoted a statement of Malik that Bukayr ibn 'Abdullah died during the reign of Hisham ibn 'Abd al-Mlik ibn Marwan. Al-Baji also supported al'Ijli's claim that Malik never heard from Bukayr directly. This leads me to the assumption, that Malik heard it via mates like a-Laith ibn Sa'ad, and this is the reason, why seemingly none except Muhammad ibn al-Hassan quoted him as a narrator, instead of using Malik's statement "a reliable source".
Explanation of the statements
Short answer
The statement of 'Umar ibn al-Khattab simply means: If there is no evidence of paternity, a child inherits only from its mother. Further, the words "Arabs" and "non-Arabs" in the statement can be replaced by "Muslims" and "non-Muslims".
Note There's a weak if not fabricated hadith saying that whoever speaks Arabic is an Arab. And since Arabic is the language of all original Islamic sources one could easily conclude that this means each Muslim needs Arabic and he at least is an Arab while for example praying based on this statement, which even if it might be fabricated or wrongly attributed still has a bit of truth. Further the Arabic peninsula was the home of all Muslims when the prophet () died, so it was often referred to as the land of Arabs, even if many Muslims were non-Arabs and also lived in this "heartland" of the Muslim Ummah.
The detailed answer
You have in your text already the explanation or interpretation of imam Malik, as he says if a pregnant woman came from the land of the enemy and gives birth in the land of Arabs... meaning in a Muslim country.
So we have a pregnant Muslim woman who came from a non-Muslim country to a Muslim country and gave birth to a child.
None in the Muslim country knows the father, so she -the mother- could claim anybody to be the father a Muslim a non-Muslim etc.. Assuming the potential father died, what is to be done?
As Malik stated in a second statement a Muslim (in this example the child) cannot inherit from a non-Muslim (potential father) by sunnah (see for example in Sahih al-Bukhari).
But since the woman lived somewhere else and the pregnancy was not known, how could anyone in the Muslim country verify whether her claim about the father was correct when she claimed he was a Muslim from the city?
For this reason, 'Umar ibn al-Khattab decided not to let the child inherit from a potential father because there is simply no evidence that the child's father is a Muslim.
The case would be different if we assumed that she had been away for a few months, but her pregnancy was known and therefore the possible (Muslim) father was also known.
Here the explanation as stated by az-Zurqani in his commentary on al-Muwatta:
( عمر بن الخطاب أن يورث أحدا من الأعاجم إلا أحدا ولد في العرب ) بمجرد دعوى القرابة وإقرار بعضهم لبعض ، فأما إذا عرف ذلك وثبت بعدول مسلمين فذلك كالولادة في أرض الإسلام يتوارثون بذلك ، قاله ابن القاسم عن مالك .
('Umar ibn al-Khattab refused to let anyone inherit from the non-Arabs except for one who was born among the Arabs.) (Source)
simply by claiming kinship and acknowledgment of some of them to each other. But if that is known and proven by the non-Muslims, then that is like being born in the land of Islam and they inherit from it. Ibn al-Qasim reported this on the authority of Malik.
Further, he explained the rest of the sunnah.com quotes as follwos:
( قال مالك : وإن جاءت امرأة من أرض العدو فوضعته في أرض العرب فهو ولدها يرثها إن ماتت وترثه إن مات ميراثها في كتاب الله ) السدس أو الثلث
(Malik said, "If a pregnant woman comes from the land of the enemy and gives birth in arab land so that he is her (an arab) child, he inherits from her if she dies, and she inherits from him if he dies, by the Book of Allah.")
One-sixth or one-third
( والأمر المجتمع عليه عندنا والسنة التي لا اختلاف فيها والذي أدركت عليه أهل العلم ببلدنا أنه لا يرث المسلم الكافر بقرابة ولا ولاء ) أي عتق فإن كان رقيقا أخذ ماله بالملك لا الإرث
(The generally agreed on way of doing things among us and the sunna in which there is no dispute, and what I saw the people of knowledge in our city doing, is that a Muslim does not inherit from a kafir by kinship, clientage (wala'))
That is, emancipation, and if he is a slave, his money is taken by ownership, not by inheritance.
( ولا رحم ) عملا بعموم لا يرث المسلم الكافر
(or maternal relationship)
In accordance with the general rule, a Muslim does not inherit from an infidel
( ولا يحجب أحدا عن ميراثه ) لأن من لا يرث لا يحجب وارثا كما
(nor does he (the Muslim) overshadow any (of the kafirs) from his inheritance.)
because he who does not inherit does not withhold an heir as well
( قال مالك وكذلك كل من لا يرث إذا لم يكن دونه وارث فإنه لا يحجب أحدا عن ميراثه ) إذ لا معنى لحجب من لا يرث .
(Malik said, "Similarly, someone who forgoes his inheritance when he is the chief heir does not overshadow anyone from his inheritance.")
as there is no meaning to withholding from someone who does not inherit.
The statement as presented in the version of Muhammad ibn al-Hassan a-Shaybani
We must be aware that this version is somewhat the Hanafi version of al-Muwatta', since imam Muhammad ibn al-Hassan not only quoted what he heard from imam Malik, but added to each hadith or statement the views and ahadith he has learned in al-'Iraq from his teachers abu Hanifa and abu Yussuf etc., so here just the translation of what he has quoted, I've added it because it explains the situation even more as I suppose:
أخبرنا مالك، أخبرنا بكير بن عبد الله بن الأشج، عن سعيد بن المسيب، قال: «أبى عمر بن الخطاب، أن يورث أحدا من الأعاجم إلا ما ولد في العرب» ،
Malik informed us from Bukayr ibn Abdullah ibn al-Ashajj from Said ibn al-Musayyab say, ''Umar ibn al-Khattab refused to let anyone inherit from the non-Arabs except for one who was born among the Arabs."
قال محمد: وبهذا نأخذ، لا يورث الحميل الذي يسبى وتسبى معه امرأة،
Muhammad said: And from this we take that, a pregnant woman who is taken captive and a woman is taken captive with him does not inherit any inheritance.
فتقول: هو ولدي أو تقول هو أخي، أو يقول هي أختي، ولا نسب من الأنساب يورث إلا ببينة إلا الوالد والولد، فإنه إذا ادعى الوالد أنه ابنه وصدقه فهو ابنه، ولا يحتاج في هذا إلى بينة إلا أن يكون الولد عبدا فيكذبه مولاه بذلك، فلا يكون ابن الأب ما دام عبدا حتى يصدقه المولى، والمرأة إذا ادعت الولد، وشهدت امرأة حرة مسلمة على أنها ولدته وهو يصدقها وهو حر فهو ابنها.
So you say: He is my son, or you say: He is my brother, or he says: She is my sister, and there is no lineage that can be inherited, except with evidence for the father and the child. If the father claims that he is his son and he believes him, then he is his son, and he does not need proof in this matter unless the child is a slave and his master disbelieves him in that. He is not the father's son as long as he is a slave until the master believes him, and if a woman claims the child, and a free Muslim woman testifies that she gave birth to him and he believes her while he is free, then he is her son.
وهو قول أبي حنيفة والعامة من فقهائنا رحمهم الله
This is the opinion of Abu Hanifa and the majority of our jurists, may Allah have mercy on them
