What is the ruling on selling a car in installments after purchasing it from an office directly in the buyer's name to save on registration fees, while ownership of the money remains with the questioner and her nephew's son and the office receive a commission? And if it is unlawful, are there any legitimate ways out, and what are the implications for the beneficiary regarding the capital and profits from transactions that have taken place in this manner?

There is no objection to this transaction if it adheres to the conditions of a Murabaha contract for one who commands a purchase, meaning that your nephew first buys the car and takes possession of it, then sells it in installments. As for the car remaining registered in the name of the office and then being transferred to the buyer to save fees, this does not affect the validity of the sale, because it is a legal procedure for documentation, and the sale is established upon the completion of the contract.