In order to bill the shipping charges to another account, you would need to specify who to bill the shipping charges to while creating your shipment.
To do so, create a shipment as you normally would.
When you arrive to the Services page (the page that shows you all service levels and prices) there is a section at the top right where you can indicate your Billing Options.
Click on Standard Options. A Billing Options window will appear and you'll be able to enter either a FedEx or UPS account number to bill the shipping charges to.
Note: You cannot currently bill the shipping charges to another Secureship account.
