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Prophet Muhammad (ﷺ) is a descendant of Abraham through Ishmael. This is stated in the Quran:

Quran 2:127-129 And [mention] when Abraham was raising the foundations of the House and [with him] Ishmael, [saying], "Our Lord, accept [this] from us. Indeed You are the Hearing, the Knowing. Our Lord, and make us Muslims [in submission] to You and from our descendants a Muslim nation [in submission] to You. And show us our rites and accept our repentance. Indeed, You are the Accepting of repentance, the Merciful. Our Lord, and send among them a messenger from themselves who will recite to them Your verses and teach them the Book and wisdom and purify them. Indeed, You are the Exalted in Might, the Wise."

Quran 14:37 Our Lord, I have settled some of my descendants in an uncultivated valley near Your sacred House, our Lord, that they may establish prayer. So make hearts among the people incline toward them and provide for them from the fruits that they might be grateful.

The above verses establish that the descendants of Ishmael settled around the House (Kaabah) and that a Messenger would be raised from among them who would bring them a Scripture. The Messenger that Abraham prayed for in 1:129 refers to the Prophet Muhammad.

A hadith is related from the Prophet in Tafsir Ibn Kathir:

أَنَا دَعْوَةُ أَبِي إِبْرَاهِيمَ

I am the supplication of my father Abraham

There are several Hadith where the Prophet claimed descent from Abraham, among them:

قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم ‏ "‏ إِنَّ اللَّهَ اصْطَفَى مِنْ وَلَدِ إِبْرَاهِيمَ إِسْمَاعِيلَ وَاصْطَفَى مِنْ وَلَدِ إِسْمَاعِيلَ بَنِي كِنَانَةَ وَاصْطَفَى مِنْ بَنِي كِنَانَةَ قُرَيْشًا وَاصْطَفَى مِنْ قُرَيْشٍ بَنِي هَاشِمٍ وَاصْطَفَانِي مِنْ بَنِي هَاشِمٍ

The Messenger of Allah said: Allah chose from the Children of Abraham: Ishmael. And chose from the children of Ishmael: Bani Kananah, and from the Bani Kananah He chose the Quraysh, and from the Quraysh He chose Bani Hashim, and He chose me from the Bani Hashim.

 

_{— Jami Tirmidhi كتاب المناقب ( Book of virtues )}

رَسُولَ اللَّهِ صلى الله عليه وسلم يَقُولُ ‏ "‏ إِنَّ اللَّهَ اصْطَفَى كِنَانَةَ مِنْ وَلَدِ إِسْمَاعِيلَ وَاصْطَفَى قُرَيْشًا مِنْ كِنَانَةَ وَاصْطَفَى مِنْ قُرَيْشٍ بَنِي هَاشِمٍ وَاصْطَفَانِي مِنْ بَنِي هَاشِمٍ ‏"

The Messenger of Allah said: Verily Allah granted eminence to Kinana from amongst the descendants of Ishmael, and he granted eminence to the Quraish amongst Kinana, and he granted eminence to Banu Hashim amongst the Quraish, and he granted me eminence from the tribe of Banu Hashim.

_{— Sahih Muslim كتاب الفضائل ( Book of virtues )}

Prophet Muhammad (ﷺ) is a descendant of Abraham (عليه السلام). This is evident from the Quran:

ملة أبيكم إبراهيم

[It is] the religion of your father, Abraham

^{— Quran 22:78}

It is also corroborated elsewhere in the Quran, such as:

Quran 2:127-129 And [mention] when Abraham was raising the foundations of the House and [with him] Ishmael, [saying], "Our Lord, accept [this] from us. Indeed You are the Hearing, the Knowing. Our Lord, and make us Muslims [in submission] to You and from our descendants a Muslim nation [in submission] to You. And show us our rites and accept our repentance. Indeed, You are the Accepting of repentance, the Merciful. Our Lord, and send among them a messenger from themselves who will recite to them Your verses and teach them the Book and wisdom and purify them. Indeed, You are the Exalted in Might, the Wise."

Quran 14:37 Our Lord, I have settled some of my descendants in an uncultivated valley near Your sacred House, our Lord, that they may establish prayer. So make hearts among the people incline toward them and provide for them from the fruits that they might be grateful.

The above verses establish that the descendants of Ishmael (عليه السلام) settled around the House (Kaabah) and that a Messenger would be raised from among them who would bring them a Scripture. The Messenger that Abraham (عليه السلام) prayed for in 2:129 refers to the Prophet Muhammad (ﷺ) .

أَنَا دَعْوَةُ أَبِي إِبْرَاهِيمَ

I am the supplication of my father Abraham

^{— Saheeh Ibn Hibban}

There are several Hadith where the Prophet claimed descent from Abraham (عليه السلام), among them:

قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم ‏ "‏ إِنَّ اللَّهَ اصْطَفَى مِنْ وَلَدِ إِبْرَاهِيمَ إِسْمَاعِيلَ وَاصْطَفَى مِنْ وَلَدِ إِسْمَاعِيلَ بَنِي كِنَانَةَ وَاصْطَفَى مِنْ بَنِي كِنَانَةَ قُرَيْشًا وَاصْطَفَى مِنْ قُرَيْشٍ بَنِي هَاشِمٍ وَاصْطَفَانِي مِنْ بَنِي هَاشِمٍ

The Messenger of Allah said: Allah chose from the Children of Abraham: Ishmael. And chose from the children of Ishmael: Bani Kananah, and from the Bani Kananah He chose the Quraysh, and from the Quraysh He chose Bani Hashim, and He chose me from the Bani Hashim.

_{— Jami Tirmidhi كتاب المناقب ( Book of virtues )}

رَسُولَ اللَّهِ صلى الله عليه وسلم يَقُولُ ‏ "‏ إِنَّ اللَّهَ اصْطَفَى كِنَانَةَ مِنْ وَلَدِ إِسْمَاعِيلَ وَاصْطَفَى قُرَيْشًا مِنْ كِنَانَةَ وَاصْطَفَى مِنْ قُرَيْشٍ بَنِي هَاشِمٍ وَاصْطَفَانِي مِنْ بَنِي هَاشِمٍ ‏"

The Messenger of Allah said: Verily Allah granted eminence to Kinana from amongst the descendants of Ishmael, and he granted eminence to the Quraish amongst Kinana, and he granted eminence to Banu Hashim amongst the Quraish, and he granted me eminence from the tribe of Banu Hashim.

_{— Sahih Muslim كتاب الفضائل ( Book of virtues )}

The verses of the Torah which your friend is referring to might be:

Genesis 16:12 And he will be a wild donkey of a man; his hand will be upon all, and everyone's hand upon him, and before all his brothers he will dwell."

Genesis 17:20 And regarding Ishmael, I have heard you; behold I have blessed him, and I will make him fruitful, and I will multiply him exceedingly; he will beget twelve princes, and I will make him into a great nation.

I am not aware of an interpretation that these are taken to Prophesize the religious deviance of the children of Ishmael, but even if such an interpretation exists, the Arabs were monotheists, then polytheist idolators and are now again monotheists ... so it can be subjective. As far as I am aware majority of Judaism views Christanity as Avodah Zarah (idolatory), but not Islam.

And narrated in Hadith:

Genesis 16:12 And he will be a wild donkey of a man; his hand will be upon all, and everyone's hand upon him, and before all his brothers he will dwell."

Genesis 17:20 And regarding Ishmael, I have heard you; behold I have blessed him, and I will make him fruitful, and I will multiply him exceedingly; he will beget twelve princes, and I will make him into a great nation.

I am not aware of an interpretation that these are taken to Prophesize the religious deviance of the children of Ishmael, but even if such an interpretation exists, the Arabs were monotheists, then polytheist idolators and are now again monotheists ... As far as I am aware majority of Judaism views Christanity as Avodah Zarah (idolatory), but not Islam, but you should probably have that clarified from Jewish experts.

The above verses establish that the descendants of Ishmael settled around the House (Kaabah) and that a Messenger would be raised from among them who would bring them a Scripture. The Messenger that Abraham prayed for in 1:129 refers to the Prophet Muhammad.

A hadith is related from the Prophet in Tafsir Ibn Kathir:

أَنَا دَعْوَةُ أَبِي إِبْرَاهِيمَ

I am the supplication of my father Abraham

There are several Hadith where the Prophet claimed descent from Abraham, among them:

Genesis 16:12 And he will be a wild donkey of a man; his hand will be upon all, and everyone's hand upon him, and before all his brothers he will dwell."

 

Genesis 17:20 And regarding Ishmael, I have heard you; behold I have blessed him, and I will make him fruitful, and I will multiply him exceedingly; he will beget twelve princes, and I will make him into a great nation.

I am not aware of an interpretation that these are taken to Prophesize the religious deviance of the children of Ishmael, but even if such an interpretation exists, the Arabs were monotheists, then polytheist idolators and are now again monotheists ... so it can be subjective. As far as I am aware majority of Judaism views Christanity as Avodah Zarah (idolatory), but not Islam.