Is it permissible to benefit from two bracelets that were exchanged for a gold necklace with an additional payment, then the owner of the two bracelets later backed out of the deal?

It is not permissible to exchange gold for gold with an additional sum of money. There must be equality in weight when selling gold for gold. It is permissible to sell old gold at a certain price and then add money to it to buy new gold. One must repent, annul the forbidden sale, and reclaim the contract and the amount paid.