considerably for using eSoftTools Thunderbird to IMAP Migration software to migrate Thunderbird local folders to an IMAP server. It has the capability to easily move and work with different types of Thunderbird file data on the IMAP server. Once you move your files to the IMAP server, you can proceed with backup migration and save your files in a proper format into any folders where Thunderbird stores files into the local drive.          

Know more -  Move Thunderbird Local Folders to IMAP Server