A 2-port UDP client-server works fine on the LAN. However when the client is a WAN client, there is no communication.
The UDP ports are opened by in- and outbound rules at both the server router, and the client router. Both the client and server permitting exceptions in the OS firewall also for the ports. On the server's router and client router, inbound ports are forwarded to the respective machines running the client or server.
You are quite right of course; it's not a Java case as such. Thank you for giving it some consideration though.
(And for the record as you ask, it is not related to my last question as such - that one was off an idiosyncratic wish-list - this one is outright network mechanics).