If that customer has 100's of invoices every month for the same or similar amounts, it could be a problem. If they only have one or two, then your client should be able to trace the payment to the right invoice based on the amount.
I'm a maverick when it comes to this kind of bookkeeping. :-)
Or, when the payment arrives, enter it as a prepayment. Then offset it to the new invoice when it becomes apparent that they belong together......
Or........
Or.........
:-) You get the gist, I'm guessing!