What is the ruling of the Sharia on dealing with a Christian girl who converted to Islam and lost her virginity with the questioner, and wishes to marry him, while her family rejects this marriage?

A Muslim should be a good example to others, especially to non-Muslims. If the girl embraces Islam, "Islam demolishes what came before it," and the family can be persuaded of this. The duty of obeying parents in refusing marriage to her applies unless you fear falling into sin. However, if she does not embrace Islam but regrets the indecency and improves her conduct, it is permissible to marry her after persuading the family. Should the family refuse, apologize to her gently and completely cut off all ties with her.