iCloud password fail after Apple ID change

I was previously using internet service provider (ISP) linked email address for Apple ID sign-in. I may want to move to another ISP and so changed my Apple ID email. All went smoothly except for my old iPhone 4s which runs on ISO 9.3.5. When I attempted to log out from my previous ID it wouldn't accept the password.

None of the suggestions I found in the support community relating to this problem worked. I still had access to access to the iCloud via Settings so I tried another approach and it worked.

First go into the iCloud and switch off all the apps sharing via the cloud and save them to the iPhone so only Find My iPhone is active. This may not be necessary but I did it as a precaution. Then press the Sign Out button at the bottom of the window. You should get enter password prompt for your old Apple ID. Press the "forgotten password" link which will open "Request a new password" window with the old Apple ID email already filled. Click into the Apple ID and enter your new email ID. Then enter a new password, make it memorable or make sure to write the new password down. Then press Send or Done, (can't remember exactly what it said) Now you should be able to log-in with your new Apple ID and password.

After that I logged out on my other devices already switched to the new Apple ID and logged back in the new password. I then connected my iPhone and backed up selecting merge documents from the prompt on the iPhone.

I also deleted the old Apple ID log-in from keychain.

Good Luck