You are likely needing to look for a 50/2 KLS : Hand gear change with kick start, fan cooled or a 50/2 S : Hand gear change with pedal start. The 50/2 KS had a Hand gear change with kick start and the Sachs 50/A was the "Saxonette" that is the same motor but with a two speed automatic.
50/3 LS is fan cooled with pedal start and hand shift, it is the other engine more likely as the original.
The hand gear shift can be a bitch to get synchronized to the hand shifter if your shift grip is loose from age or you have a tired cable pair.
Foot shift 3 speeds are easier to work than hand shift for getting the shift cables to behave, Sachs 50/3 BKFS is a 3 speed (kick start) and the Sachs 50/3 KLS is kick start fan cooled, if you are lucky you might find a 50/3 LFH - that is 4,3hp.
Sachs 50/4 LKH is also 4,3hp with four speed foot shift kicker, if you are fortunate to find one and can get away with a kick start on a moped where you live.