Without any scripts, you want to flip it, then change the move pivot to one of the verts (hold d and v key and move pivot to some vertex). Then make sure the translate settings are set to retain component spacing, and hold v and move one shell to snap to the other shell.
The thing I would do is rotate that UV part and then I would press on Snap button and then just move the UV part where you want it to be and you should get perfect overlay.(I'm using Blender so I'm not sure if you can do that but if you can use snap by vertex option it should make your job easier).