Hi Jonathan,
If you expect to regularly move transports between these systems, then they should probably both be in the same transport domain, with a common \usr\sap\trans. Forwarding of transport requests is generally only done between systems in the same domain (but not necessarily the same transport route).
If this is just for occasional, very infrequent requests, then I think it would be quicker and easier to just manually copy the transport request from one to the other. Find the data file and cofile from \usr\sap\trans\data and \usr\sap\trans\cofiles for the released transport from the source system, copy them to the \data and \cofiles folders on the target system, and then in STMS of the target system use Extras... Other Requests... Add, and manually input the transport request.
Regards,
Matt