Hi LINKConstruction, 

Thank you for getting back to us on this. To clarify: You are trying to assign a paid invoice for a customer to a project?

I did try to assign a paid invoice to a project by changing the customer's name to the sub-customer as a project and it worked. Both the invoice and invoice payment have been moved to the sub-customer. 

I also did try to assign an invoice that was copied from a quote and marking that invoice as paid then change the customer on the invoice, then that's when the 3 transactions broke. Is this what you are experiencing?