Open Mail.app, Right click on INBOX then select Archieve Mailbox and save it inside one folder.
Same steps need to follow for the rest mail boxes. It saves the mail boxes as .mobx format
Once we finish with archieving all mail boxes. Copy the whole archieve mail folder containing .mbox files to the system where we have Thunderbird to import these mails.
Open Thunderbird, Go to Tools – Add-ons, search for ImportExportTools and install that add-on and restart Thunderbird
Now Go to Tools – ImportExportTools – select Import mbox file – Import directly one or more mbox files
Then locate the whole archieve mail folder which you have copied from mac machine.
That’s it… In this way we can get the mails from mail.app to thunderbird
N.B. ImportExportTools having variety options, select as per the requirement