I just meant the same type of system. Of driving sprocket attachec to the wheels and wheel gear cluser attached to the axle.
You'll probably have to buy new sprockets to build a rear cluser that fits the axle. Or you could try to jury rig the existing cluster to fit.
A third option is to use the existing gear cluster from the bike, and mount them somewhere convenient. Have them rotate a shaft with a second sprocket on it and run this to the rear axle with a 1:1 ratio. This means you only need to find 1 sprocket to fit the new axle, but it adds complxity (and therefore unreliability).
Ahh a layperson :D, in that case if there is anything I gloss over, or you don't understand or whatever just let me know and i'll try to explain it better.
Please note I am a dreadful teacher, so you'll have to bear with me.