I just imported a message folder from a Local Folders in Postbox and it worked fine. I did it two ways, once with importexporttools import mbox option and once by oopying with windows file explorer. Might the message folders you're copying be IMAP account? Admittedly, I used a more recent version of Postbox, but I doubt that would be a concern.

They're not IMAP, just local folders where emails from POP accounts where automatically moved into with filter rules.

With Importexporttools, do you mean some add-on to Thunderbird, or the standard included Import tool in the Tools menu?

yes, the addon importexporttools

Which one do you mean? I can only find this one calles "ImportExportTools NG":

https://addons.thunderbird.net/en-US/thunderbird/search/?q=importexporttools&appver=128.1.0&platform=WINNT

It only offers "Import Profile" menu option which imports the entire profile. There is no mbox import option.

When I import the entire Postbox profile, it imports all the (local) folders and messages headers, but now all emails contain hexadecimal gibberish.

My earlier instructions were obviously vague. I stated i was at Local Folders. Highlight Local Folders, rightclick and there is an import mbox option.

Thanks. This way it imported the message contents as well. However, HTML formatting and all images and attachments are missing.

I suggest checking your settings in View>message body as to see if you're set for plain text. HTML, if present, is tightly embedded into the message. But you at least have the content. I'm glad for that.

Wow, it works!

After setting "Message body as" (under More button) to "Original HTML" it works (and this applies to all emails). I had no idea it was showing plain text by default for imported emails (all new incoming emails did show in HTML by default).

Thanks a lot for your help.

You are very welcome.