Well unfortunately my email server provider don't support this feature. (I'm not using gmail, Misrosoft account etc.). I will have to host my own email server anyway.
What I ended up with is simple taking all the mails from server to local machine. Store them in 2 files "inbox" and "archive" under git version control system on private remote repository. That way I can access them from other computer if I need to (that was my main concern). Anyway, thanks for the help. Have a great day, Irek