If you're using imapsync to migrate, be sure to throw it the following options:
This is what I used to migrate my mail. As for any facility to import directly from Tbird local folders? Most likely you're going to have to copy those by hand.
imapsync --nosyncacls --subscribe --syncinternaldates
Now, I don't know if you're using the same terminology here, but the Thunderbird Local Folders are local to your computer, and will not be picked up by IMAP. IMAP is for email stored on the server. The email in the Local Folders is no longer on the server (unless you copied it instead of moving), and imapsync will not be able to copy that data over.