you should find & backup your mail folder.

This folder contains sub-folders named like your theBat accounts.
Each such account physical sub-folder contains sub-folders named like the folders (defined in theBat) you had in the corresponding account.

Or to say it in another way, search the disk for files named like MESSAGES.*
Once you find such - backup the
parent - parent
folder - that should be your mail folder.

When you install theBat on another PC/disk, restore the mail folder. Then tell theBat to use it:
Options -> Prferences -> System -> Mail Directory