How to reconnect mail on Mac OS 10.11?

Question

macOS

I deleted the mail account, after a while I decided to connect it again, but when I enter the login and password from the mail, a message appears that "this account already exists." I tried to add it through the system settings (Internet Accounts), and through the settings of the Mail application - the result is the same. An active mail record works like clockwork, i.e. Mail is definitely not broken.
Actually the question is, where does the remote account still exist?

Answer 1

Reply to future questioners.
The problem may arise due to the fact that the mail address matches the address (aka login) for iCloud.
You must first log out of iCloud, then create the desired mail account, and then log back into iCloud.

Answer 2

It was the same trouble. I climbed into the Box, transferred everything offline, and then through the application settings I got into the accounts and repeated the gestures there - it helped.

Answer 3

Is there a solution to the problem? Transferring all mailboxes offline does not give me any effect.