A man married a woman who had a daughter from a previous marriage. The daughter did not grow up in his house. After that he divorced the mother and wants to marry her daughter. Is this permissible for him?
If he consummated marriage with the mother, it is not permissible for him to marry the daughter whether she grew up in his house or not. If he did not consummate marriage with the mother, it is permissible for him to marry her daughter after divorcing the mother according to the saying of Allah (Exalted be He):
...your step daughters under your guardianship, born of your wives to whom you have gone in - but there is no sin on you if you have not gone in them (to marry their daughters)
This is the view of the majority of religious scholars (Part No. 18; Page No. 223) and the opinions of those who contradict them have no effect in this regard. It should be noted that this part of the verse:
...under your guardianship
is an explanation for the predominant case and has no effect on the ruling. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.