Is it permissible for my friend to sell cars in installments on his own behalf after paying their value in cash to the supplier, and is my partnership with him permissible by me paying the price of the car in cash to the supplier, and then I sell it in installments to the customer?

It is permissible for an agent to sell the entrusted item to himself, provided the principal grants permission. If the principal authorizes the agent to sell the car to himself, the agent may purchase it for cash at the agreed price, and then sell it to another party in installments. It is not permissible for the agent to sell the car to another party on his own account unless he first purchases it for himself. As for the questioner, he may ask his friend, the agent, to agree with the customer on the price of the car in installments and take a down payment from him. Then, the questioner should purchase the car from the agent and conclude a sales contract with the customer. It is not permissible for the agent to sell the car in installments on behalf of his friend before the friend takes ownership of it.