iPhone 6s battery draining,lagging and shutdown issue

I have been using iPhone 6s for over a year now. Recently I had some battery draining problem as it would drain out from 100% to 50%within 3 hours and it was not being used enough to drain the battery. Also my screen and display were damaged due to small accident.

I visited authorised service centre and and they asked to replace the screen display and battery. After that battery was life seemed to be ok, but I found that after my phone starts reaching towards 80% battery it starts lagging and slows down its operations. At 70% battery it becomes worse to use, the phone also automatically shuts down and I have to wait till it restarts as It just shows apple logo on white screen. Service centre guys says phone ok and there is no problem with it. I am very disappointed to have this kind of support from apple flagship. Being worlds best phone for performance and Speed. This not what I expect my phone to work.

If you have any solution for above problem please suggest. My software has been updated to. 11.2.6