According to Shariah law, a "hibah" (gift) is only considered complete when the gifted item is transferred to the recipient, along with ownership rights. This means that the donor relinquishes all control over the item (including residence, belongings, possession, and the ability to control its use).
Therefore, in the situation described, ownership of the house depends on whether your father transferred possession of the house. If he transferred possession of the house to your mother when gifting it to her, then it becomes her property. However, if he did not transfer possession of the house it remains under his ownership and should be distributed among the heirs according to the laws of inheritance prescribed by Shariah.
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دلائل:
الدر المختار مع رد المحتار: (كتاب الهبة، 690/5، 691، ط: سعيد)
"(وتتم ) الهبة ( بالقبض ) الكامل ( ولو الموهوب شاغلا لملك الواهب لا مشغولا به) والأصل أن الموهوب إن مشغولا بملك الواهب منع تمامها وإن شاغلا لا فلو وهب جرابا فيه طعام الواهب أو دارا فيها متاعه أو دابة عليها سرجه وسلمها كذلك لا تصح."
Allah the Almighty knows best.
Darul ifta Al-Ikhlas, Karachi.