Need to Switch from Mac Thunderbird to Apple Mail. But First I want to backup Mac Thunderbird. How Can I Do It?
Have you tried Time Machine to Backup your emails?

A more elaborate procedure is explained here: https://www.youtube.com/watch?v=Cd2YaBCXpaM

You can also opt for third party applications: http://mac.softpedia.com/get/Utilities/Mail-Backup-X.shtml

I hope this helps. Thanks