What is the ruling on buying a house from an adopted son, knowing that he does not inherit according to Sharia?

Sponsoring and taking care of orphans are among the best deeds. However, adoption, which is the attribution of an outsider to the adopter, is forbidden (haram) and does not entail any of the rulings of sonship, such as inheritance.

Regarding the house, if the man acquired ownership of it through a valid gift or an enforceable will, he is permitted to sell it, and you are permitted to buy it. However, if his acquisition of ownership of the house was not valid, then he is not permitted to sell it, and you are not permitted to buy it.