I was thinking something like Cito or KG - built in former East Germany I think, so Czech Republic sounds OK. The motor seems to have a "timing chest" between the magneto and the crankcase - just the sort of place that you might expect to find timing gears and cams in a four stroke. There's even a plate on top where the tappets might mount. Cito/KG had valves at the front. Many two strokes used magnetos driven directly off the end of the crank, but this one is not on the same axis as the crank. In a four stroke it is geared down 2:1 and so is offset from the crank.
The reason I'm interested is that there was an unsuccessful Australian bike of the early 1920s called the "Aussi Also" (witty name if you know a little French and some Australian slang). The two stroke Aussi Also was a very similar layout to this engine (shaft drive, magneto in front), and was said to be a two stroke built from a four stroke. The reason it never ran properly was said to be lack of crank case compression, as you might expect from this type of conversion. Of course it has always been thought that the (bad) conversion was done in Australia, but I wonder if this engine tells us differently?
See if you can get the owner to take of the magneto and "timing cover" off, and show us what is inside.
I'll attach a photo of a Cito, taken here in Australia of all places.
Leon
