2013 logic board 2009 case

Late 2013 27" iMac

I have some severe health issues and was forced to move into a house that would be more conducive to my situation.

While moving my brother walked out to his truck to get the last of my things (it was getting dark) someone was in the process of trying to steal my 2013 27 inch iMac.

When they saw him they took off running and dropped my iMac on the front seat of his truck which ultimately fell in the ground and cracked the screen.

I live on a fixed income and can't afford a new screen but I found someone on Craigslist that's selling a 2009 27" iMac that needs a logic board. Is it possible to put a 2013 logic board and all it's components in a 2009 iMac case?

When I had my health I worked on PC"s for about 20 years so I'm confident I can do the work myself.

Thanks