I happen to have both so I tried them out.
My Swedish military issue alcohol stove fits inside my East German mess kit, no problem.
The pot in the mess kit will go into the Swedish windscreen all the way, as long as the pot handle (bail) is straight up. To fold down the pot handle, you will need to file a little bit off the slots on either side of the windscreen.
The "frying pan" part of the mess kit will not fit into the windscreen unless you bend out the sides of the windscreen a few mm.
If you want to fold the pan handle down against the windscreen, the hooked part of the handle hits the windscreen so you would have to do some cutting or filing to get it to work.
Fortunately the windscreen is aluminum and therefore soft. So, it *can* be made to fit if you're handy with tools and don't mind fiddling with it. But if there's any way to get the Swedish kit it will of course work better.
Note that I'm referring to the *East* German mess kit as you mentioned. I also tried a *West* German mess kit which I happen to have (I accumulate gear, what can I say?) -- it is a little bigger and won't work at all with the Swedish windscreen.
Hope this helps. Cheers.