One step can do it:
Set Field [Invoice::CustomerID ; Portal::Customer ID ]
Either place a transparent button in your portal row that covers the entire row or group all of your portal row fields into a button to perform the above script.
Note: Most businesses want a copy of the customer info recorded in their invoice so that future changes in customer contact info don't alter previous invoices. Once you've set a customer ID field to the correct value other fields in Invoice can use auto-enter field options (either looked up value or the calculation option) to copy over the customer name and contact info.