What is the ruling on ordering goods at a cash price when they are unavailable or there isn't enough money to purchase them, and requesting the money be sent to acquire them, knowing that the customer will take them in installments?

If the situation is as we understood from the question, that you buy a commodity with a man's money and then sell it to him at a higher price (installment price) to gain the difference without his knowledge, then this is forbidden and impermissible. This is because you are his agent, and it is not permissible for you to increase the price on him unless you agree with him on a known commission for the agency.