Ayatana Webmail is an application that integrates your webmail into MATE, Xfce, LXDE and other desktop environments. It displays notifications about incoming mail, shows the number of unread messages and displays subjects in the Messaging Menu. The Launcher item also has a quicklist that provides quick access to your mail folders. It also allows you to quickly compose a new message. Ayatana Webmail starts automatically, all you have to do is to enter your accounts settings in the configuration dialog.
For further info please see https://tari.in/www/software/ayatana-webmail/