Are you using any backup plugin? How are you exporting users?

If you have PhpMyadmin, you can export 4 tables (starting with PREFIX_fep_, PREFIX is your database table prefix) and import in your new database.
You can even use any migration plugin from wordpress which support custom table.

This plugin does not have any export/import feature build in.

Note: Test exported data before deleting from your website.

Which version of the plugin you are using?
Did you imported users as well?
import front-end-pm folder from you wp-content/uploads directory.

Then try to send a message to any other user. After sent please check again if all messages shows or only last message.
Let me know.