So my wife was having a similar issue with an iPhone 6s I bought for her in Nov 2015. It would shut off at 20 percent battery all the time. We have AppleCare+ so we figured we would take it in one of these days to get it resolved. Last night I saw the article:
https://www.apple.com/jp/support/iphone6s-unexpectedshutdown/ and let her know so we can resolve first thing today.
Early this morning she called customer support and let them know about the issue and the article. The tech was unaware of the article and ran diagnostics on the device which came back fine. My wife provided details to him about the article and he went ahead and scheduled an appointment at a local Apple store.
We go to the Apple Store at the designated time and the local technician is clueless. They did not read the notes left by the phone technician, had no clue about this new battery replacement article, and wanted to run diagnostics again. After we got them up to speed, they replaced the battery no questions asked.
Long story short, provide the article and everything should move forward.