Hello,
we have a similar set up for a credit card. All the payment for expenses go to a credit card company.
We have 2 service providers: A1 - for payments to employees and C1 - payments to a credit card company for their expense.
In order to post an expense to the credit card company we maintain configuration in the Transfer to accounting.
In here for C1 we specify the credit card company vendor number, and that is the number used to post the payment for a travel expense when the service provider = C1.