Is it permissible, Islamically, for a husband to designate an apartment for his wife as a usufruct (right to use) after his death, with its ownership transferring to his son after the wife's death or her marriage to another man, knowing that he has another wife and other children?

The bequest of dwelling in the apartment after the husband's death for the duration of the wife's life or until her remarriage is a bequest of usufruct. This is impermissible in Islamic law for an heir and falls under the general meaning of the Hadith: "Indeed, Allah has given every rightful person his due right, so there is no bequest for an heir." This is because usufructs are properties that are exchanged for compensation. Similarly, his bequest that the apartment devolve to his son is a bequest to an heir, which is impermissible in Islamic law. These invalid bequests are not enforceable unless the rest of the heirs consent to them.