Sorry for the error.

"MT" means what?

You haven't specified what authentication method is set, but it is typically oauth in which case the answer is again going to be https://support.mozilla.org/en-US/questions/1477809#answer-1693122. Even though Thunderbird prompts for a password, it only saves the oauth token.

MT = Mozilla Thunderbird

Once again.. I'm not asking for password for Google IMAP account. In my case Google password is only need to connect Google Calandar by plug-in. Google then requires confirmation through its additional window (browser, not through MT checkbox), but is secondary issue.

Main problem is with password from simple mail account from xxx domain. And what does it matter what the authorization method is for this account??? Regardless of whether it would be a regular password or SSL, after entering it correctly (and setting up the account) and confirming the "checkbox" it should be remembered (otherwise the server will check the authorization and reject it, right?). In the meantime I enter it, check my email, close the program, open it and it asks for the password again. Additionally, if the password was remembered it should be in the password manager, but it is not.

It DOES matter what authentication is used.

Part of the whole point of oauth is your password doesn't get saved - a token is stored for your future access, not the password. This will not be changed.

To learn more https://www.techtarget.com/searchapparchitecture/definition/OAuth