Move to Level doesn't work

I have 2 levels, one empty one filled with content(a landscape too). I want to move a part of the landscape to the other empty level. However, this is proving problematic.
When I click on a part of the terrain, I see a “landscapeProxy” object highlighted in the world outliner.

The current level is the empty level, and the filled level is loaded too. With the move level tool activated, I click on pieces of terrain, and square patches are highlighted, but they are not moved to the empty level!
I’ve used the move tool in other projects and it worked, here it doesn’t.

And yes I made sure that no part of the terrain was actually moved, I turned the visibility on/off for each of the levels & loaded them separately. I just can’t find a way to move patches of terrain to the other level.