Despite all of my efforts to re-run /scripts/convert2maildir with option 3 (Convert partially converted mail accounts), there was still a huge mailbox file for the Sent folder in the user’s account (/home/user/mail/bgsnow.com/problem_user/Sent). Of course, the maildir folder .Sent (/home/user/mail/bgsnow.com/problem_user/.Sent/) did not have any of the mails from the Sent mailbox file.

After googling for some time and trying third party scripts to no avail, I have turned to a simple solution. I have created a directory /home/user/mail/bgsnow.com/test/. This should represent the mail directory for a fake email account test@bgsnow.com. Then I have copied the Sent file from the user which has problems (/home/user/mail/bgsnow.com/problem_user/Sent) to this directory and re-run /scripts/convert2maildir. This created the needed maildir directory .Sent (/home/user/mail/bgsnow.com/test/.Sent)  which I copied directly to the mail directory for the user with problems (/home/user/mail/bgsnow.com/problem_user/).

This fixed the problem for me