What can I do if I forgot the Apple Account used on my locked iPhone?

My brother's iPhone was locked for a long time due to vertical connection on the screen, so he forgot his phone's passcode. He tried the wrong passcode many times. That's why his iPhone got locked.

Now it's asking for his old Apple ID to unlock his iPhone. He forgot which Apple ID was logged into his iPhone and even he forgot which email he used to open his Apple ID.

[Re-Titled by Moderator]