It is possible from the control panel to create a backup of the entire site and download it, including mail.
Proceed as follows:
- Access your CPANEL and locate the JetBackup item, access the "Full Backups" function, select the backup to export and click on "generate download".
This will start the backup generation process. - Once the backup is ready, the "download" item will appear.
By clicking on Download you will be able to locally save all the content of the site and mail.