Extracted from: http://support.apple.com/kb/ht2980#mail
To manually back up Mail messages (emails)
To back up entire mailboxes (where Mail stores messages), such as your Inbox, follow these steps:
1. Quit Mail if it’s open.
2. From the Finder’s Go menu, choose Home.
3. Open the Library folder.
4. Copy the folder “Mail” to your backup location, such as a different volume or burnable disc.
Important: Do not remove the Mail folder from ~/Library. If you’re backing up to the same
volume, hold the Option key as you drag the folder to make a copy instead of moving it (a “+”
Copying Mail to a Local Folder
1. Create new folder locally
o To copy e-mails locally you must first create a local folder.
o In the left pane of the Thunderbird window select Local Folders.
o Go to the File menu, click New, and then click Folder.
o Next, Assign the folder a name, and then select Local Folders
o Click on the OK button to create the folder.
2. Move e-mail to new local folder
o Now, select the e-mail messages that you wish to move offline and have saved in your local folder.
o Once selected (highlighted), right-click on the PC or Control+Click on the Mac and select Copy To,
o Then select Local Folder, then select the new folder.
Install the following Addon in Thunderbird and restart the client.
In thunderbird client, right click on the account , click ImportExportTools , select “Export all the
folders ( with structure )”, select OK.