If you want to change the customer on an invoice you will have to duplicate the invoice to a new Quote.
Change the Customer on a Quote
To change the customer on a quote, you must first remove all the IMPRINTS from the order. Then refresh the page.
Once all imprints/artwork have been removed you can change the customer by clicking the double arrows next to the customer name, as shown in the image below:
NOTE: You will have to remove all the artwork/imprints from the Quote before you can change the Customer. (Since any existing artwork will be directly linked to that customer.)
After removing the Artwork refresh the page.
Once you have changed the customer, you can add those imprints back as "Derivatives." ("Duplicate / Clone Imprint.")