If you actually just trying to make a current Customer into a Job of another "Customer" then goto:

Customer Center

Select the dropdown for the New Customer &Job and select Add Multiple Customer and Jobs.

In this screen you can move around your Jobs and Customers as needed at one time and not have to try and mess with it on a one to one basis as it takes longer and can be frustrating to get it to toggle right with the dang diamond.

I hope this helps all, I have the same client in two different places and this is the way I can keep them straight ( categorize by type of client(this becomes the company)).

Robin