For the backup of Gmail account you can try Gmail backup tool they help to create the backup of your Gmail account they backup your account in a few steps like.
The first step is to install and run software
Second, Gmail username and password is required for connecting to your Gmail account therefor
The third step is to select whose mail you want to backup
The last step is a select export option (EML, EMLX, MSG, MBOX, PST) file format that as per requirement and the export data accessed to any version of outlook, apple mail, window live mail and other client and select output directory where do you want to save and then click process now button .