Is it considered forbidden for a mother to ask her son to register half of the house in his name, knowing that he is responsible for her and his divorced sister and her six children, and that she had previously sold land that she had registered in his father’s name, and distributed her inheritance?

Registering half of the house in the husband's name, if it is to be owned by him during the mother's lifetime, is a gift that is not permissible unless there is a justifiable reason for تخصيص (singling out), such as need, chronic illness, a large family, or the husband's service and care for the mother. However, if the registration is for him to own it after the mother's death, then it is a bequest to an heir, and a bequest to an heir is not permissible.