Is the deceased's share of the house, which his father relinquished to him, to be divided among the deceased's heirs, or the father's heirs, or the mother's heirs, based on the deceased's will: "If it is established in Sharia that what my father gave me is not rightfully mine, then look to the ruling of Sharia regarding its division," and the mother's claim that the house is from her private funds and that she gave half of it to the father?

Half of the house registered in the name of the deceased father is considered his property. The wife's claim of ownership is not accepted without proof. If the writing for the three children means their taking possession after death, then it is a bequest to an heir (wasiyyah li-warith) which is not executable except with the consent of the other heirs. If they do not consent, half of the house shall be divided among the heirs of the deceased father, including the son who died after him. In case of dispute, the matter should be referred to the Sharia court. The mother's share is one-sixth due to the presence of siblings, as stated in the Qur'an: {But if he has brothers [and sisters], for his mother is one-sixth}. The remainder goes to the full siblings by way of 'asaba (agnatic succession), with the male receiving the equivalent of the share of two females, as stated in the Qur'an: {And if they are brothers [and sisters], men and women, then for the male is the share of two females}. There is nothing for the father's brothers or the sons of the full brother, as they are excluded by the full brother.