Is it permissible in Sharia to purchase goods from Al Arabi Bank, which it owns and are located in Al Fozan's warehouses, and then appoint Al Fozan to sell them and receive their price?

If the goods are genuinely owned by the bank, there is no objection to purchasing them from the bank through murabaha or other means, provided that the Shariah controls for murabaha sales are observed. The majority of scholars have stipulated that the sold item must be taken possession of before it is resold. Possession varies according to the nature of the item. The Hanafis are of the opinion that for movable goods, clearance (takhliya) is what is considered. Once the goods enter into your ownership and you have taken possession of them, you are then permitted to authorize the company to sell them or dispose of them as you wish.