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He'd have been better off inflating his front tyre properly!
The BMW K series engines werent very nice motors. Not all that powerful, rough in a way that the Japanese hadnt been sinde the 60s. The shorn down 3 pot 750 version was actually a more pleasant unit.
Probably better to pinch the head for a conversion than transplanting the whole K motor.
I seem to remember reading that the 3 cylinder required a balancer shaft, so ended up rather smoother running than the intrinsically better balanced 4 cylinder 1000cc which hence didn't "need" the balancer shaft. Caveat: this is what I was told / read as I've never ridden either.
My much more modern and much missed Triumph 3 cylinder, which I think did have a balancer shaft, was lovely. My 4 cylinder Saab also had a balancer shaft and was super smooth, close to my old Triumph 6 cylinder

Someone used to pick her kids up in one of those, when daughter was at senior school