Once a client has paid his invoice in full, you can send him back the invoice (there is no limit on the amount of time you can send an invoice) marked "Paid" with the paid-to-date amount and balance due listed at the bottom of the invoice.

You can also add a comment in the Notes field stating that the invoice is paid.

Moreover, when sending back the invoice by email you can specify that the invoice serves as a receipt for the payment made.