Is it permissible to execute the husband’s will, which grants his wife the right to usufruct the residential house and rent it out throughout her life, provided that the house is divided according to Sharia after her death, knowing that the house exceeds one-third [of his estate], and that he has no heirs other than his brothers and sisters, and the husband mentioned that registering the house in the names of both spouses together is not permissible according to Sharia, taking into account the jurisprudential rule "no bequest to an heir"?

The husband's bequest of the house to his wife after his death is not valid unless approved by the heirs, based on the Prophet's (PBUH) saying: "There is no bequest for an heir." If his intention was to register the house in her name during his lifetime such that she would own it after his death, then this falls under the ruling of a prohibited bequest. However, if his registration of the house in her name during his lifetime was with the intention of it being a gift (hibah), then this is permissible, provided he did not intend to disinherit other heirs, and it is completed by her taking possession of the house during his lifetime. This bequest is not a lifelong grant ('umra) because a lifelong grant occurs during the lifetime of the grantor and not after his death.