I don’t know for sure but I can think of 3 reasons why it would not work. It may not fit in the space in the 6s (it’s pretty tight in there) It may not connect electronically. Each camera model is made for a specific model of iPhone. The 6S may not be able to work the camera (focus and OIC).
It sounds like your phone is in Low Power mode. Got to Settings-Battery and there should be a slider to turn it off. I believe the phone will go into Low Power mode automatically if the charge is very low. Hope this helps. There may also be a problem with the battery.
Check: Settings-Battery-Battery health. If it’s below 90% (my 6s was at 88%) you may be able to get a free battery replacement from Apple. I did mine a few months ago and it’s like having a new phone. Check this site: https://www.apple.com/support/iphone6s-unexpectedshutdown/