What is the ruling of Islam on a man's bequest to his family that his wife may live in his house for the rest of her life after his death, as long as she does not marry another man?

A bequest to an heir is not permissible and will not be executed unless approved by the other heirs after the death of the testator. This is based on the Prophet’s (peace be upon him) saying: “Indeed, Allah has given every rightful person his due, so there is no bequest for an heir,” except that Al-Daraqutni added in a narration, which Ibn Hajar deemed good: “Unless the heirs wish so.” As for a gift to the wife, it is permissible before the illness leading to death and becomes effective if she takes possession of the gifted item.