Hello all! Well after some testing I got this:
1) It is managesieve related problem.I message put in some folder via sieve - TB & Outlook don`t see this message.
2) TB have a workaround described by Jonathan:mail.check_all_imap_folders_for_new must be set "true" in your Thunderbird configuration. It's an advanced setting
Tools->Options->Advanced->General->Config Editor 3) I don`t have a clue how fix it for a Outlook. Any hints? -- Best regards, Proskurin Kirill