Chosen Solution
The new battery I just received from ifixit will not fit the internal connectors on my model a1549. The old battery pops right back in place, but the new one will not connect. Any suggestions? I am positive I purchased the battery recommended by ifixit.
On the back of the housing, where the small text is, you should see the model number of your device (hopefully it’s the original housing). If it is indeed an iPhone 6S, like you selected for this question, then it should say A1688/A1633 and not A1549. I suspect there is confusion between the model phone you have, what was ordered or what was delivered. Either way, contact iFixit Support and they will help you out.