Is it permissible, Islamically, for the son to be given to the questioner's brother to raise him and attribute him to himself, knowing that this has already happened and the son is four years old, and that his brother and his wife are attached to him?

A father's gift of his son to someone for adoption is invalid شرعاً (religiously). A father does not have the right to dispose of his child by selling or gifting him. Islam has forbidden adoption and attributing a child to other than his father, as Allah Almighty says: "Call them by their fathers' names; it is more just in the sight of Allah." Attributing a child to other than his father is one of the gravest sins. Therefore, it is not permissible to register the son in the brother's name or attribute him to him. However, it is permissible for the brother to sponsor and raise him without adoption or attribution.