It would be tricky, but I don't think it's impossible.
Of course you need to add the Height Map and the Terrain Map as you did before, in your new computer, and if you already had objects in the map you were working on (if they weren't meshes you downloaded and added to your map, if you did you wil have to place those new meshes in the new computer as you did before), I'm not quite sure if they re-apear on not. What have you been able to do so far?