How to add a button to check the emails of my domain?

Based on my comment in the Question, I tested the solution of adding a menu item that opens an iframe in its screen.

As expected, Gmail doesn’t allow to be displayed in an iframe. But a regular Horde Webmail does work.

add_action( 'admin_menu', 'embed_webmail_wpse_91871' );

function embed_webmail_wpse_91871() 
{
    // Reference: http://codex.wordpress.org/Function_Reference/add_menu_page
    // Check it, specially regarding the last parameter ($position), i.e.: 6
    add_menu_page( 
        'webmail', 
        'Webmail', 
        'edit_pages', 
        'webmail', 
        'webmail_iframe_wpse_91871', 
        'http://i.imgur.com/Vk42k.png', 
        4 // position, just after Dashboard
    );
}

function webmail_iframe_wpse_91871() 
{
    ?>
    <div class="wraper">
        <iframe 
            src ="http://example.com/webmail" 
            width="100%" height="700" />
    </div>
    <?php
}

Results in:

Particularly, I’ve never seen a plugin for doing webmail inside WordPress.
In my opinion:

• seems excessively complex for something that simply needs a new browser tab to work.
• sounds like embedding Outlook into Word.