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Yes this is possible. Even if you have corner studs in the existing building you can put new one's in and dismantal the back/side wall that is an issue and either plywood it up or use the matarials that you removed to redo the wall. If it were me i would reframe the end getting shaved off first and then cut off the excess. I bet one of those handy oscillating saws would work perfectly in tight corners to get precise cuts.
If needed or wanted for a good laugh at the neighbors expence you could even leave the top half of that wall open and just wire it in against predators so they hear every egg song, cluck, and crow loud and clear!!!!
I must share my favorite quote by Mark Twain: "It's a wonder God suffers so many fools, what with lightning so cheap".
After reading all the posts and hearing the happy ending, I wonder if you should call the local newspaper and get a 'human interest' story write up about the wonderful people who came to your aid? Patriotism is on the rise right now and I think other people would be moved and gratified by the ending to this story. Of course it wouldn't hurt to be factual about what the neighbor did, now would it?