What is the religious ruling on a fostered girl remaining in the couple's home after the husband becomes aware that she will be an unmarriageable kin (mahram) to him when she grows up? And is it permissible to return her to the orphanage?

Muslims must care for foundlings, and whoever takes in a foundling and raises them removes the sin from everyone. It is not permissible to adopt a foundling and fabricate a lineage for them. Jurists have set conditions for a foundling to remain with the person who found them: justice, Islam, maturity, and residency. If these conditions are met in the man and his wife who took the girl from the foundling home, there is no justification for returning her to the orphanage. The fact that she is a stranger does not prohibit caring for her, but it is forbidden to interact with her as a daughter if she reaches the age of tahrim (when marriage to her would be forbidden). However, while she is young (less than two years old), it is permissible to interact with her.