It is possible to use Third Party Billing when shipping with FedEx so that shipping charges (and optionally duty charges) can be billed to a third party FedEx account number.
To use Third Party Billing, from the FedEx settings page, expand the Advanced Settings, accessible by clicking the cog icon on the bottom left hand side of the screen. You will see a field titled Third Party Billing, as shown below. Enter your third party account number in this field and save. Change the Payment of Shipping Charges option to set who pays the shipping cost.