Then, you are hit on the head by an additional invoice. Since first and additional invoices appear different, this is not call for suspicions from the recipient. Such additional invoices are sent mostly to companies where officers automatically pay the bills which look like they are from a government organization, without checking. But the government has nothing to do with this. A well-organized business is working.
Payment is asked from both the sender and the receiver.
It is explained to both that payment is not a customs fee, but for paperwork which supposedly is prepared when a shipment crosses the border. However, if you send or receive the same shipment by regular mail, nobody will ask additional payment from you. In addition, the shipment passes through the same customs office. This is a regular lie. You have already paid for delivery and do not need to pay anything additional.