Is my husband entitled to claim the full amount (40,0) that he spent on building and equipping the second floor and additional finishes, in the event of selling the house or upon inheritance, and is the ruling of the husband's father to pay only half the amount (20,0) considered permissible, or is he not entitled to claim any amount spent?

Since the husband’s father gave permission for construction on top of his house but did not grant him the airspace, this construction is considered a loan (ariya) that terminates upon the father’s death, and the father has the right to end it before then. If the loan terminates, the structure, whether demolished or standing, becomes due to the husband for its value. Then, the structure reverts to the father or his heirs, and the husband participates as an heir. If the father’s compensation to the son equals the value of the construction, the son has no right to demand more. Otherwise, he has the right to demand the remaining value, while being keen on honoring his father and pleasing him.