Confirmation of receipt during the fair exchange

Is there a way to confirm the delivery of an item to the recipient e.g(bank payment)? Let’s say there is a trust third party in the protocol. The sender’s side (honest) says that it sent the payment, the recipient’s side says that it did not receive anything (lies). Conversely, if the sender’s side lies that it sent the payment and the recipient’s side honestly declares that it did not receive anything. Is there a way to verify this to a TTP without "investigation"?