What is the ruling of Islamic law regarding our father's verbal sale of a property to our sister's husband, where the full amount has not been paid, despite a previous arbitration council, and what is our duty as his daughters concerning our sister's husband's insistence on owning the property in light of our mother's opposition?

If it is confirmed that the men's council affirmed that your father owns 40% of the house and your sister's husband 60%, this is considered a rescission of the sale for the portion that the buyer was unable to pay for, which is permissible according to the most authoritative opinion. The seller has the right to rescind the contract if the buyer is in financial difficulty or procrastinates.

If your sister's husband denies the agreement, the default is that the house belongs to him, and you must prove the agreement.

If your father is of sound mind, he has the right to waive his share or demand it. If he is not mentally competent, his money may not be disposed of except in a way that benefits him. Your father is entitled to 40% of the house if your sister's husband acknowledges the agreement, or if you prove it with the testimony of two witnesses, or with one just witness and an oath.