I had the same problem. After screen replacement it's not working.
I fixed it accidentally though.
So here's what I did:
I installed IOS 11 Beta and within IOS 11 the touch ID was all good. I was very exited to have my touch ID working again. The only problem was- the IOS Beta was not stable and my phone was restarting all the time, so I had to downgrade back to IOS 10.
I was pretty sure that I'm losing the touch ID again.
Now I'm back on latest IOS 10 and The touch ID is working perfectly fine with my after market screen.