What is the ruling on money deposited by a mother in the bank in her daughter's name, telling her it would be hers after her death?

If a mother wishes to grant a sum of money to her daughter, a gift conditioned on death is subject to the rules of a bequest (وصية). A bequest to an heir is not valid, due to the Prophet Muhammad's (peace be upon him) saying: "Indeed, Allah has given every rightful person his right, so there is no bequest for an heir." In this case, the sum would be part of the estate and all heirs would be entitled to it. However, if the mother completes the gift to her daughter during her lifetime, and transfers ownership to her such that she disposes of it as she disposes of her own private funds, then the gift is valid, and ownership transfers to the daughter. It should be noted, however, that it is not permissible to prefer some children over others in a gift unless there is a legitimate شرعي justification, such as need or poverty.