Is it permissible for the grandfather to transfer a portion of the villa to his second wife, knowing that it was (purchased) with the contribution of his first wife, and is it religiously permissible for the family to reclaim what was transferred?

If the grandfather meets the conditions for disposing of his property, he may gift whatever he wishes from his wealth to his wife, provided he does not intend to harm the heirs or deprive some of them. No one has the right to object to his gift. The conditions for disposal are: reaching puberty, being free, having full mental capacity, and attaining maturity.

The grandfather's relinquishment of his residential home to his wife can be viewed in two ways: 1. Bequest (Wasiyyah): If the relinquishment is in the form of a bequest, meaning she does not own it until after his death, then it is treated as a bequest to an heir. 2. Gift (Hibah): If it is in the form of a gift, there is a difference of opinion among jurists regarding its validity. The method of possession for such a gift, according to the view that deems it valid, is by emptying the house of his belongings and leaving it for the wife.

As for the grandmother's contribution to building the house, this is a claim that can be proven by admission or evidence. If you have what proves it, you have the right to demand your share. In this case, it is preferable to resort to the judiciary to resolve the dispute.