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QB Desktop will not allow you to do a journal entry with A/R and A/P on the same journal entry which is what you need to do in this case.
The best way to do this is to create a bank account in QB called 'Clearing Account' and use that to offset the invoice and bill. Receive payment on the customer's invoice and deposit it to the newly-created bank Clearing Account. Then, pay down the bill by the same amount using the same Clearing Account. You now have the invoice paid and a balance remaining on the bill that you can pay. This works if the bill amount exceeds the invoice. If the invoice amount exceeds the bill, reverse the process - pay the bill and then receive payment on invoice.