Playing multiplayer with a buddy, who due to his host advantage in the slow late game managed to sneak the system with Dimensional Mirror from under my nose. Going to battle with him is an option, but I would want to deal with the issue with least casualties.

As far as I see, one cannot build a second Dimensional Mirror by default. If the system is lost to someone else, can I, the initial researcher, build another one, or is it lost to me unless I do battle with the claimant?