Is it permissible to exchange a sold gold necklace for other gold, whether of equal or lesser weight with the price difference returned in cash, after the sale has been completed, the payment received, and the buyer has departed?

It is permissible to exchange gold for gold, weight for weight, with immediate possession in the same session. However, exchanging it for less than its weight while returning the difference in weight in cash according to its value is a matter of scholarly disagreement. Malik and Al-Shafi'i prohibited it, while Abu Hanifa permitted it, based on the permissibility of selling gold for silver with a surplus. If the surplus is not realized by calculating the gold at its true value, then the matter is closer to permissibility. The best course of action, to avoid disagreement, is to annul the first sale and then conduct a new sale.