Does the house that the father gifted to one of his sons and registered in his name, and which the son can sell and buy an apartment with, fall under the father's estate after his death? And what is the share of each of the heirs (the mother, three males, and eight females) if the house is valued at 22,500 Libyan Dinars?

If the father had given similar gifts to his other children as the house he gave to one of his sons, or if he singled him out for a pressing need (such as disability, seeking knowledge, or a large family), and the gift was valid (with the father's full legal capacity and the son's possession of the house before the father's death), then it is permissible. However, if he did not give to the rest of the children and there was no justification for singling him out, then this is not valid, as it was narrated from An-Nu'man ibn Bashir (may Allah be pleased with them both) that the Prophet (peace be upon him) said: "Fear Allah and be just among your children."

Assuming the house is an inheritance, its value is known, and the heirs are identified: - The wife's share (mother of the children) is one-eighth as a fixed share due to the existence of a inheriting descendant, as Allah Almighty says: "But if you have a child, then for them is one-eighth of what you leave." - The remainder is divided among the sons and daughters, with the male receiving the equivalent of the share of two females, as Allah Almighty says: "Allah instructs you concerning your children: for the male, what is equal to the share of two females."

However, if the mother mentioned is the deceased's mother (and not his wife): - Her share is one-sixth as a fixed share due to the existence of a child, as Allah Almighty says: "And for his parents, each one of them is to have a sixth of what he leaves if he has a child." - The remainder is distributed among the sons and daughters, with the male receiving the equivalent of the share of two females.

Warning: Matters of inheritance are serious and complex, and a mere fatwa is not sufficient; rather, they must be referred to the Sharia courts for investigation and to ensure that there are no other heirs, wills, debts, or rights that take precedence over the rights of the heirs.