What is the ruling on selling a commodity in installments at a price higher than its cash price, then a third party buys it at a price lower than its cash price, and sells it again at a price higher than its purchase price, with the possibility of returning it to the first seller? And is this action correct or incorrect?

There is no objection to selling in installments with a price increase if the conditions of sale are met. There is also no objection to Tawarruq (buying an item in installments then selling it for less to obtain cash), provided that the item is not sold to the original seller (which is the forbidden Bay' al-'Inah) or to someone colluding with him. Selling it to someone colluding with the seller is considered a triple trick to commit usury, and it is the most reprehensible and severely forbidden form of 'Inah. So, if you buy an item and then sell it in the market to someone other than your brother, there is no objection. However, if you sell it to your brother (and he was the original seller or colluding with him), then this is a forbidden trick to commit usury.