A man is married and has children, and he wishes to marry a second wife. He is finically solvent and physically apt. Is it permissible for him to marry with a female foundling? He will provide her with a noble life that she is dreaming of, but he conditioned on her not to have children from him, as her origin is unknown. She agreed to this condition and she wishes to marry this man.

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.

There is no harm on you to marry this female foundling especially if this is with the purpose of keeping her chastity, spending on her and the like. If she agrees to marry you with the condition of not having children, the marriage is correct, as having children is her right and she renounced it by herself. However, it should be noted that whenever she wishes to withdraw this condition, she is permitted to do so. In this case you have the choice either to keep her as a wife and have children with her or divorce her.   

Allaah Knows best.