The issue I see is that you are issuing an invoice for an item or service that will be an open customer transaction until it is paid. Ergo, you would need to reverse the transaction with a credit note immediately to get this to work, but then what do you match the inbound invoice against?
You would need to set a default invoice code to identify the payment to the one customer account. I believe that is possible. There are no document fot handling pre paid actual transactions, but would a proforma invoice be sufficient?