Here is my solution if your iPhone 6s is stuck on the “connect to iTunes” screen.
Here’s what happened to me on or around July 30th, 2016:
Need to dump vacation photos from wife’s iPhone
iTunes says phone has update, would I like to download. (yes)
The update downloads (took a long time)
iTunes says “extracting update”
iTunes says “installing update”
After a while, iTunes says “install unsuccessful”
Phone screen shows “connect to iTunes”
iTunes says, “Something is wrong. You need to update or do a factory reset.” (shivers)
Phone will not update.
Hold Home button and Wake button for 10 seconds until Apple logo appears. After 2 seconds, the logo is replaced by the “connect to iTunes” screen.
Got on Apple chat support. We were disconnected after 20 minutes. New person didn’t have past 20 minutes of conversations. Hung up.
Search internet for “iPhone 6s photo recovery” and get “Wondershare – Dr.Fone for iPhone 6”
Wondershare – Dr.Fone for iPhone 6 is software that is free to download. It will connect to your phone and let you know if the data is recoverable. If you want to recover it, you have to pay something like $50 for the partial version of the program and more for additional recovery options.
I just wanted to see if the data was recoverable so I download the software.
When I run the software and plug in the phone, the software says something along the lines of, “Your phone is not in a readable mode. Would you like to restart.” I click yes.
THE HOME SCREEN POPS UP!!!!!
I upload all the photos to the cloud. Save all contacts and backup passwords.
From the phone, I use the update function.
The phone updates.
I plug it into iTunes and it works fine.
I hope this helps you.