Is it permissible to marry a Christian woman who had previous relationships, and is now on her way to Islam, knowing the marital infidelity she committed before marrying her?

For a marriage to a Kitābiyyah (woman of the Book) to be valid, she must be chaste. If this woman married after abandoning illicit relations with men, and the marriage was conducted with the permission of her guardian from among her people, and in the presence of witnesses, then the marriage is valid. You should not hold her accountable for sinful relationships she had before marriage. We advise you to be kind to her and treat her well, so as to encourage her towards Islam. Perhaps Allah will make you a cause for her guidance, for "that Allah guides one man through you is better for you than possessing red camels."