This is about mailboxes, Kieran?
If so, Thunderbird did, and still does, used the mbox format; so nothing has changed there.
Frankly, since Pegasus can handle mbox, as well as its own native format, I'd don't know I'd even bother to convert. I think I'd make a copy of the folder/s I wanted to move--you'll find it/them in:
C:/Kieran/Application Data/Thunderbird/Profiles/<Some random number>/Mail/Local Folders
After that, I'd make a new mailfolder inside Pegasus's GUI and choose "Unix" format. Pegasus will then give that file a name consisting of a (random?) number and the file extension .MBX. If you rename your mbox file to the same name and drop it into the same place in the hierarchy, on the C: drive where the mailfolder resides, it will then over-write it, and next time you open the program you'd see the mails there. From there you could use drag-and-drop within the program's GUI to move the mails.
But go with the converter, if you find it easier. I haven't used Dawn, but it seems to be what most people use. The Thunderbird format hasn't changed, so there's no problem there.