If you are looking for the best tool to migrate Thunderbird local folders to an IMAP server, consider using eSoftTools Thunderbird to IMAP Migration software. It has the capability to move and work with various 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 store your files in a pure format or in any folders where Thunderbird saves files into the local drive.          

Know more -  Move Thunderbird Local Folders to IMAP Server