I've heard different opinions about this issue, what’s the stand of Islam on a Muslim woman marrying a non-believer? What if the man claims he'd convert to Islam to be able to marry the Muslim woman? Please provide a reliable reference for each claim of yours, since I’m not interested in personal opinions.
According to jafari Fiqh:
A Muslim man is allowed to marry a Christian or a Jewish woman in temporary marriage. Based on precaution, it is obligatory to refrain from marrying a non-Muslim woman in permanent marriage. A Muslim man is not allowed to marry, neither permanently nor temporarily a non-Muslim woman who is not among Ahlul Kitab. Based on obligatory precaution, a Muslim man must refrain from marrying a Zoroastrian woman, even temporarily. As for a Muslim woman, she is not allowed to marry a non-Muslim man at all. (See the question-answer section below.)
Ref: www.sistani.org (no.390)
About claim, the parents of Girl and Girl have duty to do enough research about belief and morals of the man. There are many Hadith insisting on research about the man to have two main attributes: 1- Belief (practicing the rules of Islam) 2- Having good morals. If had this two property the marriage should be accepted according to Islam and non-Islamic terms should not be set. For example the wealth and properties of man.
Answer to your question is in
Surah Al-Baqarah - Aayat 221 [Chapter No. 2 Verse No. 221], as stated follows:
And do not marry polytheistic women until they believe. And a believing slave woman is better than a polytheist, even though she might please you. And do not marry polytheistic men [to your women] until they believe. And a believing slave is better than a polytheist, even though he might please you. Those invite [you] to the Fire, but Allah invites to Paradise and to forgiveness, by His permission. And He makes clear His verses to the people that perhaps they may remember.
A Muslim woman can not marry a non-Muslim man.
The following verse declares that the Kuffar (disbelievers) are not lawful husbands for them, nor they lawful wives for them. Kafir is a general term for non-muslims and includes everything that is not Islam: Judaism, Christianity, Polytheism, Atheism, Henotheism, Monaltry etc.
يا ايها الذين امنوا اذا جاءكم المومنات مهاجرات فامتحنوهن الله اعلم بايمانهن فان علمتموهن مومنات فلا ترجعوهن الى الكفار لا هن حل لهم ولا هم يحلون لهن
O you who have believed, when the believing women come to you as emigrants, examine them. Allah is most knowing as to their faith. And if you know them to be believers, then do not return them to the disbelievers; they are not lawful [wives] for them, nor are they lawful [husbands] for them.
Apart from this, marriage to Mushriqeen (polytheists) is specifically forbidden, and Shirk is in everything that denies Allah and his Oneness or sets up partners or equals with him:
ولا تنكحوا المشركين حتى يومنوا ولعبد مومن خير من مشرك ولو اعجبكم
And do not marry polytheistic men [to your women] until they believe. And a believing slave is better than a polytheist, even though he might please you.
http://quran.com/60/10 : ... And if you know them to be believers, then do not return them to the disbelievers ("alkuffar"); they are not lawful [wives] for them, nor are they lawful [husbands] for them. ... and as far as I know, Christians and Jews are accounted as disbelievers in Quran.