Thanks again for your very quick and very helpful support, Stanislas !
I copied the both map files from my computer to the other one and started the game. Worked like a charme !
We played (and are still playing) AoE2. I think it would be a very helpful feature, if the 0AD client will copy (download) the game files automatically from the server. Like in AoE2 where also my own maps are recognized and shared automatically with all other players before starting a multiplayer game. If the security concerns are too big, maybe the server could read/open the game details, transmit the data to the clients and they could save those defined and formatted data back into a game file. Would be a bit more complex, but block all hacks or mis-usages of the XML files. Or (as 3rd idea) the server opens the XML file and checks the validity of the content, generates a hash and the clients can download the file from the server. Before starting the game, the hashes are shares and validated between server and client.
A automatic-sharing-solution should be implemented, because most other players will be deterred by the current way of sharing maps (just my two cents).
This ticket can be closed and marked are successfully answered. Thanks again !