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As far as the open bill goes, since the vendor received the payment for that already, you can remove that open bill. Follow these steps to delete a bill:
1. Go to Expenses.
2. Choose the bill from the Expense Transaction Lists.
3. In the Accounts Payable register in the Charts of Accounts, find the bill and select it.
4. Within the report, choose the bill.
5. In the Bill window, select More at the bottom of the screen, and click Delete from the pop-up menu.
6. Click Yes, confirming to delete the bill.
For the customer's invoice, removing the total amount on the invoice should not affect your accounts receivable. However, I do advise getting with your accountant to confirm that this works best for your business. If you don't have an accountant, you could connect with a ProAdvisor specialist. They do offer a free consultation to businesses. Simply enter your zip code and search to find one near you.