What is the religious ruling on an oral will that was not witnessed by anyone, in a case where the father willed to his wife that she should take the rent from his properties after his death, knowing that these properties are registered in the names of the children and nothing is registered in the wife's name?

There is no bequest for an heir, according to the Hadith: "Indeed, Allah Almighty has given every rightful person their due, so there is no bequest for an heir." Accordingly, there is no consideration for the wife's claim that her husband told her to take the rent of the shops after his death. Nor is it permissible for him to write the shops in the name of some heirs to be their property after his death. All of that reverts to the inheritance and is divided among all heirs according to their prescribed shares, unless they agree to approve what the father bequeathed. As for the deceased's pension, there is a detailed explanation: it may be part of the inheritance or a gift from the entity that pays it.