Expense payment for cc transactions

Credit card purchases for business expenses.
I have enabled Expense Claims, and created an Expense Claim Payer (the credit card).
I created an expense claim, paid by the Expense Claim payer (credit card), and listed the gl expense account (office expenses) in the Account field in the detail line.

All good so far (I think), as the summary shows the Expense claim amount in the Liabilities of the Summary, and can also drill down in the Expenses to see the individual expense line amount as well.

Making the Payment for the expense claims is where I am not following.
At the time to pay the cc statement (manual reconcile, not imported or anything like that), how do I record the cc statement payment to offset against the Expense Claim Payer? In the Payments screen, the Payee drop down does not list the Expense Claim Payer?

Am I missing a setup step? Or am I not following the correct method?

You should use a Credit Card account to record purchases made by a company credit card, not an Expense Claim Payer

The card fee is then an expense recorded as a purchase and the balance payment as an inter-account transfer