You want to export email messages from Gmail to EMLX. I recommended Mailvita Gmail Backup Tool for Mac and Windows. This application is export Gmail Account to Multiple file formats such as EML, EMLX, PST, MSG, MBOX, etc. This software is help to backup Gmail Account to Local Drive. Users can easily to backup emails from Gmail Account with Attachments. It is supports all email clients such as MS Outlook, Apple Mail, Thunderbird, Windows Live Mail, Power Mail, etc. Download the free demo version of the application. Supports all Mac and Windows OS versions.