Is there functionality in the AR module to issue a CM which triggers a refund back to the customer?

Summary:

We have overbilled a customer which they have paid the invoice. The customer is now requesting for a refund of the overpayment.

Normally when we create credit memos, it goes as a credit on the customer's AR account, and reduces the amount they pay us towards their next invoice. In this case, however, they are requesting that we pay them back in cash, as we're not anticipating future invoices with them. We also need to adjust or decrease our revenue. Is there functionality in the AR module to issue a credit memo which triggers in AP module to issue a payment back to the customer? Or do we need to request a payment through AP, which would be