All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If what you mentioned about this woman is confirmed that she apostated from Islam and converted to Christianity after being a Muslim, then it is not permissible for you to befriend her or have affection to her. Allaah Says (what means): {You will not find a people who believe in Allaah and the Last Day having affection for those who oppose Allaah and His Messenger, even if they were their fathers or their sons or their brothers or their kindred.}[Quran 58:22]. However, this does not mean to stop advising her, rather you should continue to call her to Islam and you may seek the help of the Muslim brothers who are in charge of Islamic centers, as Allaah may make her regain her senses thanks to you.
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Finally, it should be mentioned that it is not permissible for this woman to foster this child - if he is still at the age of fostering - since she is an apostate. Therefore, it is an obligation on his father to endeavour to take him from her using any means to achieve this, and he should not let her influence him in his religion and moral conduct.