This is Bob. I'll do my best to help.
I'm guessing that the iPhone is wanting you to sign in using your Apple ID after the update. If this is true, and you don't remember your Apple ID password, this should help.
First, you may or may not know what your Apple ID is - it is actually an email address and it should appear on the screen that is requiring your password.
Next, go to https://appleid.apple.com
you should see where to login with your Apple ID and password, please enter the email address from the first step. Then enter a password ***** you would have used, you might need to try a few. At some point you should be presented with something like "Forgot your password?" - click that link and follow through the steps to regain access to your Apple ID.
Once you've successfully reset your Apple ID password, go back to the iPhone and proceed with the post-update setup by logging in with your Apple ID and password.
I do hope this helps. Let me know if you have any questions.
Just following up on this. Was my advice useful, or do you need more assistance. I want to make sure I've done all I can to help.
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Thank you so very much,