iOS 9 upgrade frozen at "Slide to upgrade"

Solution 1:

Apparently this is a known problem when updating from iOS 7 devices straight to iOS 9.

Apple has posted a workaround, which should help you out:

If the Slide to Upgrade screen won't go away after you update to iOS 9.

I'm not posting the text verbatim, in case Apple improves their answer.

Note that you will need a computer to connect the device to, to make a local backup.

Edit 2015-09-23

Apple have released iOS 9.0.1 which according to this report

address issues users have experienced with the Setup Assistant app getting stuck on “Slide to Upgrade.”

I am guessing it will still be necessary to connect to a computer any iOS devices that are stuck at "Slide to upgrade".

Solution 2:

If you havent saved your pictures,you can actually save them. When you're on the screen that says,update completed(before the choose wifi screen), you can connect it to your computer and it will recognise the iphone,you can click the ''trust this computer'' as if you iphone was on main screen. There, when your computer see's your phone,you can look up the files and copy them to the computer, Then do the restore since the pictures are now saved in the computer.