How is the estate of a deceased mother to be divided, given that she bought a piece of land for 500 pounds, which one of her sons paid, and then that son borrowed the same amount from his brother, who later built a three-story building on the land?

The amount the son paid on behalf of his mother is considered a gift, unless he intended otherwise. The amount the brother borrowed from his brother is considered a debt, unless the lender waives it. The land is considered the property of the mother, and the building erected on it by the son is considered a loan (عارية), which is terminated upon the mother's death according to the majority of jurists. Upon the termination of the loan, the owner (of the land) is given the choice between ordering the borrower to demolish the building or paying its value as dismantled. The land alone should be appraised, then the building should be appraised as dismantled, and both parties share (in the value) according to their respective proportions.