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 have already clarified that if a woman who was never pregnant had milk and she breastfed a child 5 times his fill, and this was during the period of two years, then she becomes his suckling mother. For more benefit, please refer to Fataawa 92362, 91200 and 86312.
A suckling by which the child has suckled his fill is when the infant sucks the nipple of the woman and then releases it (when he doesn't feel like sucking any more) with his own will, and he may do that more than once in one session.
Therefore, if that girl had really suckled five times according to what we mentioned, then your wife has become a suckling mother for her and you will be a Mahram to her even if the milk she suckled was not produced after your wife had given birth to your child. That is because she is the daughter of your wife, so she is like your step-daughter.
However, if there is any doubt regarding this suckling whether or not it renderers the mother a Mahram to the child, then in this case, your wife is not considered her suckling mother because, in suckling, it is a condition that it should be confirmed in a manner that proves that the mother becomes a Mahram to the child.
However, we do not know what you mean by the adoption that the Islamic authority judges to be lawful. If you mean the valid suckling that renders the suckling mother a Mahram to the child she suckled, then there is not doubt about confirming the mother as a Mahram to the child by suckling him. Also, if you mean taking care of orphans and sponsoring them, then this is a matter which the Sharee’ah encourages and Allaah gives much reward for it.
But, if you mean adoption itself, in a way that this girl is traced back to you, then this is forbidden. For more benefit, please refer to Fataawa 82371 and 84422.
Allaah Knows best.