Is it Islamically permissible to sell air conditioners in installments to those in need—by purchasing them from them at a price higher than what the merchant sold them for, after they have gone to get them appraised in the market without transporting them—and what should I do about previous transactions that occurred in this manner?

The sale of a commodity by a person on credit and then purchasing it from the same buyer for a lower cash price is "Bay' al-Inah" (a specific type of sale). The majority of scholars have deemed it forbidden due to its trickery designed to circumvent usury (riba). They cite the hadith of Aishah (may Allah be pleased with her), who strongly denounced a woman who engaged in such a transaction, considering it to nullify jihad unless repentance is made.

The permissible way out of this is for the buyer to sell the commodity to someone other than the original seller. This is known as "Tawarruq" among the Hanbalis, and the majority of scholars have permitted it, provided there is no apparent intention of riba.

As for past forbidden sales of this type, repentance is obligatory. For any such sales that are still ongoing, it is not permissible to take back more than what was paid in cash, based on the Prophet's (peace and blessings be upon him) saying: "Whoever conducts two sales in one sale, then he gets the lesser of the two or usury."