Is it permissible to marry a Christian girl who believes in Islam but holds some different beliefs, and what are the recommendations to draw her closer to Islam?

This relationship between a man and a woman is not permissible for him, nor is there a legitimate marriage contract between them that Islam would approve. It must be severed, or the man should marry the woman. It is permissible to marry women from the People of the Book, and one can benefit from fatwas related to inviting non-Muslims to Islam.