Can I change an invoice that has been paid with a credit?

Good day, Zippygal.

Did you record a credit memo for the credit? If so, we can open the transaction and assign it to the correct customer. 

Here's how:

1. Go to Customers > Customer Center.
2. Select the customer's name where the credit was added.
3. Double-click the Credit Memo and select the correct customer from the CUSTOMER:JOB drop-down.
4. Click Yes when prompted of the changes.

Once done, go to the correct customer and apply the credit to the invoice by creating a Receive Payment. Just open the invoice and click the Receive Payment button.

For a visual guide, you can check the screenshots below:

I'm adding this article for reference about credits: Give your customer a credit or refund in QuickBooks Desktop for Windows.

Should you have any other questions, please let me know and I'll get back to you the soonest. Thanks.