Is it permissible to marry a girl who offers to embrace Islam in exchange for marriage, knowing that she has a past?

It is impermissible for a Muslim man to marry a non-Muslim woman unless she is from the People of the Book (Jewish or Christian) and chaste. Chastity is a condition, based on the Almighty's saying: "and the chaste women from among those who were given the Scripture before you." It is preferable for a Muslim man to marry a righteous Muslim woman. However, if the woman from the People of the Book is chaste and there is hope for her to embrace Islam, then marrying her might be commendable. One must ascertain her condition before marriage, as she might promise to embrace Islam after marriage and then fail to fulfill that promise, or the marriage might fail due to her apostasy or bad character.