Is it permissible for the father to register the floor built by his son in his own name, and the floor built by his brother in his own name, provided that only the first and second floors are part of the inheritance, with the knowledge and approval of all siblings?

It is permissible for a father to grant the air space of his house to his children who built upon it, provided that he is equitable among his children in the grant. This means he should estimate the value of the area upon which construction occurred and give a similar value to his other children. If justice is not achieved, then the grant is void, and the house becomes a loan (عارية) that terminates upon the father's death. However, if the rest of the children agree to the preference and allocation, then it is permissible, and the floor belongs to the one who built it, as the reason for prohibition—which is instigating animosity and severing kinship ties—is then absent.