Setting up a new BU in PS Billing and PS AR and have a question about Customers

We've always just used one business unit for everything. Now that we are implementing PS Billing, we have a need to setup a new BU for billing and AR. What we are not sure about is how the customers link. In other words, the customers have a setid assigned to them, so how do we assign a setid on the customer to the new BU setup in AR Billing? Do we have to setup new customers to go along with the new BU's for AR and Billing?