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Hello. My name is Michael. I can help you with your question.
Can you please tell me the exact wording of the message you get?
What kind of phone is this? Or is it on your computer?
It will as long as you are using the same account on all devices.
However, when you set the password, I would do it from a desktop computer. Once you do this, it will be in effect for your Google account across all devices.
One possible problem is that if you have devices accessing your Google account while you are changing the password, the device with the old password ***** keep trying to log in with the old password. Then, by the time you get to that device, it may have locked you out from invalid login attempts. To avoid this, remove the google account from each device, then set your password ***** the desktop computer and go back to each device and add the google account back.