Is it obligatory to relinquish a right to a house purchased with ill-gotten gains to a brother, especially since he sees accepting this house for himself as a solution for his ill-gotten gains, keeping in mind that "Allah is good and accepts only that which is good"?

We understand that the father bought the house with money donated by the son and registered it in his wife's name. If it was a gift to her, then the house is hers, and the son has no right to it. If the father is still alive, the house is his property regardless of the official registration. If the father dies and the house is his property, then it is an inheritance for all heirs. If the father bequeathed it to his wife, then a bequest to an heir is invalid unless the other heirs approve it.

However, if the money used to buy the house was unlawful (haram), this does not make the house itself unlawful. Rather, the amount of the unlawful money must be expended for the benefit of Muslims, the poor, and the needy to purify it. If the donating son has both lawful (halal) and unlawful money, his donation is considered to be from his lawful money. But if the donor possesses only unlawful money, and the father was poor, then there is no obligation to dispose of the amount given to him, because it is one of the channels for expending unlawful money. If the father was not poor and was unaware of its unlawfulness, then he must expend the amount of the unlawful money to make his enjoyment of it permissible. As for someone who is poor and receives some unlawful money, they are not obligated to expend an equivalent amount, because it is permissible to give unlawful money to the poor, and it becomes lawful for them.