How to transfer an Invoice that is paid under one customer to another customer and mark it as paid on quickbooks desktop?

I'm trying to clean up some accounts. There is a transaction which is under example: Michigan Caterpillar. This transaction has been paid and reconciled. However, this transaction should be under Caterpillar. Michigan Caterpillar and Caterpillar are two different vendors. 

What is the best way for me to move it from Michigan Caterpillar to Caterpillar?