There are several possibilities. One would be that each is using POP setup, meaning that sent messages are stored on their PCs. Another possibility is that they have set Thunderbird to save sent messages on their PCs. And I am confused: you say it is a shared account, but you later say there are three shared accounts. Are there three different email addresses, or just one email address?

Thank you for your reply. 1. POP won't solve the problem. We need that sent emails from one person could be read by others. 2. There's 1 account, but 3 people who use this account. Sorry for misunderstanding.

What I meant is that the problem may be there because you, or others, are using POP. All accounts must be IMAP for this to work. Settings for each PC should be reviewed. If all are set the same, then all sent messages will be viewable.

All use IMAP. All sent mails are visible only in web view. But they're not visible in Sent folders of other colleagues, that didn't sent this specific mail. Everyone sees only those letters, which they've sent from this very device.

I believe the index is built from emails that Thunderbird 'sees', so try File>offline and select a download option to pull in all messages.

I tried this. It doesn't work. And relaunching of program also doesn't help.