When we acknowledged that the invoice is not a partial invoice, PO is not available to invoice the remaining quantity. You could do an accounting cancellation on the invoice, delete it and generate a new invoice by selecting the correct answer for the question.

That doesn't help when we do not realize the mistake when it is done. We're training a new A/P person and it gets caught when we get a 2nd invoice for the same PO and by then we've paid the first invoice so it can't be accounting cancelled.

I come across this periodically, we will have 2 receivings one invoiced and the PO tagged as fully invoiced
AP is unable to enter the second invoice to match to the 2nd open receipt.

for whatever reason the PO once tagged as 'fully' invoiced will not allow the open receipts to have an invoice applied to it to be paid.
reopening the PO unlocks the receiving, but not the invoicing portion.

What I found was there is an extra step that needs to be done.
1. purchasing\Orders\Close and reopen orders - to reopen the closed PO (this opens the receiving but doesn't change the invoicing)
2. purchasing\Orders\Orders - go back into the PO and notice that under the 'Management' the received line is now partially received, and the Invoiced is still tagged as 'completely' invoiced and .. these are greyed out so can't change anything here...

go to the 'Lines' tab, double click on the line and you should get a pop-up

Select 'Yes'
This changes the 'Fully' invoiced indicator to 'partially' 
resave the PO.

3. Purchasing\Orders\Invoices\Invoice control
The missing open receipt was still not available for me to select under the receipts tab but the PO is now available under the PO tab with a drop down showing the missing receipt info and the 'Order' can now be pulled into the invoice to match to be processed.