Yes..you can go after who ever you want; however,your success will depend upon any contracts in place which may hold others including your receiver harmless in the event of nonpayment by your client. Go after him though..and good luck..
You can ultimately seek payment from any party who had beneficial ownership of the goods while in transit. It stands to reason that if either the shipper or receiver had rights to claim from you or your insurer for damages, that they would be obligated to pay you.
I always bill both the shipper and the receiver and in the last year ALL invoices have been paid from one party or the other. They always seem to get together and sort out who the cheque will be sent by.