Backup and restore emails in cPanel webmail – Roundcube
You can use one of the following links to access cPanel webmail: http://yourdomain.com/webmail
Click the email which you want to backup.
Click “More” then choose “Download (.eml)”.
Emails will be downloaded as .eml* file.
Click the “Gear Icon” and choose “Import messages”.
Select the backup file and click “Upload”.