Is my brother, who works in a gold shop, committing a haram act or not?

The fundamental principle is that there is no harm in selling gold or engaging in work related to it. However, it is a condition for the sale of gold for gold, or silver for silver, or gold for silver, or gold for banknotes, or silver for banknotes, that the exchange takes place in the same session of the contract. If the type is the same—such as gold for gold—then equality in quantity is also required.