Tidbits write at https://tidbits.com/2018/09/10/mojaves-new-security-and-privacy-protections-face-usability-challenges/

Apple is enhancing OS security to boost OS privacy
Apple has been inching down this path of protected files in macOS since it introduced Gatekeeper and sandboxing. With each release, Apple has tightened the sandboxing screws to limit the traditionally near-unfettered access of apps. However, application sandboxing as we’ve seen it so far applies only to apps downloaded from the Mac App Store and offers no protection to apps installed from any other source.
Mojave extends these protections in three key areas across all applications on your Mac:
• Access to the camera and microphone
• Access to certain private data stores (beyond those protected in High Sierra)
• Inter-application communications with Apple events

What does this mean for Mail Archiver?

The last item in the list is affecting Mail Archiver. You need to grant access to each mail client that you archive from (Mail, Outlook). If you archive to Filemaker or Evernote you need to grant access to those 2 apps, too.

When Mail Archiver the first time tries to talk to Mail you will get the following dialog:
You need to click on the "OK" button. If you click on the "Don't allow" button Mail Archiver can't get data out of Mail.

For version 4.3 you will get one error message per app if it doesn't have permission to access the app. On older versions you will get a generic error -1743 for each AppleScript that runs. And there are a lot of AppleScripts in Mail Archiver!

And of course Mail Archiver can't get the any mailboxes:

To fix this you need to quit Mail Archiver and go to the System Preferences and then Security & Privacy. There you need to add the checkbox for Mail Archiver and Mail:

After restarting Mail Archiver the mailboxes for Mail will now load: