iPhone has been updated successfully but why is it still stuck on connect to iTunes? I only wanted to restore my iPhone 7plus, so I downloaded iOS 10.3.2 and 10.3.1 from a trusted site.
I have made backup and all is okay, then when I attempt to restore my iPhone using the downloaded version, at the end of restoration process, my iPhone stuck on connect to iTunes!

I have connected the iPhone to my computer and it shows a message: There's a problem with iPhone which needed to be updated or restored!!
I tried to use update with the both iOS versions and it says iPhone has been updated successfully. However, it is still stuck on connect to iTunes?

What's wrong? How do I proceed from here?
Those versions are no longer signed.

Apple has stopped signing iOS 10.3.1 so it will not work to downgrade to. You need to use iTunes to update back to iOS 10.3.2 and your phone will work again.