I'm here to explain why you're seeing this behavior.
When you turn a Sales Order into an Invoice then change the Customer, the Rep is going to disappear. This is because the link is created for the original Customer and the Rep. I recommend creating a new Sales Order for the Customer and then creating the Invoice. Here's a Community Article that provides detailed steps: Create An Invoice From Sales Order in QuickBooks Desktop.
If you have further questions or concerns, don't hesitate and reach back out! Wishing you and your company continued success.