What is the ruling on selling by installments if an external party comes forward, pays the price of the commodity in cash to the seller, and then collects the installments from the buyer with an increase? Is this considered usury? And what is the correct Shariah-compliant method for selling by installments between the seller, the buyer, and the third party who pays in cash?

Selling a commodity by installments is permissible, and the seller is allowed to increase the price in exchange for deferment, and to take guarantees such as a guarantor or collateral. As for a third party paying the price to the buyer in exchange for the buyer repaying him with interest, this is usury (riba), unless the third party genuinely purchases the commodity and it enters into his possession and responsibility, and then sells it to the buyer by installments. In that case, he becomes the creditor.