Is it permissible to marry a Hindu girl who claims to have converted to Islam for the sake of marriage, knowing that she lost her virginity through fornication?

It is not permissible for a Muslim man to marry a disbelieving woman, because of Allah’s saying: "And do not marry polytheistic women until they believe." Therefore, your marriage to a Hindu woman is invalid, and cohabiting with her is fornication. Her conversion to Islam merely for the sake of marriage is not sufficient, because one of the conditions of "La ilaha illa Allah" (there is no deity worthy of worship except Allah) is certainty that negates doubt, and Islam is submission to Allah and disavowal of polytheism. We advise you to seek a Muslim woman of good religious character and to cut off your relationship with this girl unless she embraces Islam sincerely.