You connect ShipTrax to a router. That then makes available the AIS messages on port 10110, which you can access from anywhere in the world, as long as your router's firewall allows an incoming connection. You could then run something like AIS Dispatcher on the remote host to record the TCP/IP AIS messages, and replay them later back to ShipTrax.
The ShipTrax software also has it's own recording facility, much like Radarbox.