Is it permissible for a father to buy his son's merchandise while being unaware that it belongs to his son?

The money your parents gifted you becomes yours, and the items you bought with it are also yours, allowing you to sell them to your parents. For a sale to be valid, it is not required for the buyer to know the owner of the commodity. Therefore, you may sell the item to your father at the agreed-upon price without deception or fraud.