Is it permissible to purchase a phone in installments from a person who buys the item based on the buyer's request, then sells it to him for an increased, fixed price that does not change with delay or early payment, knowing that this person did not own the item before it was requested?

The transaction mentioned is a Murabaha sale for the one who orders the purchase, and it is permissible if it adheres to the Sharia guidelines. There is no harm in selling a commodity for a deferred price that exceeds its spot price. This is not usury (riba) because time has a share in the price, and this is what the majority of scholars have concluded.