Markus Echterhoff

This plugin is as simple as it is useful. Add the widget or use the shortcode <code>[you-have-a-new-message]</code> anywhere to display a notice if the currently logged in user has new messages. The notice links to the user’s inbox as a convenient and omnipresent shortcut.
Message texts can be configured via widget interface and shortcode parameters, e.g. <code>[you-have-a-new-message single="new message" multiple="%s new messages"]</code>.
<h4>Translations:</h4>
<ul>
<li>German</li>
</ul>

You Have a New (BuddyPress) Message

Notify users about new BuddyPress messages (widget & shortcode)

smsfly

This plugin sends SMS messages to the administrator’s or client’s phone about events on the site, including order tracking in the WooCommerce plugin, Contact Form 7 plugin, and more through the “SMS-fly” service
Features:
SMS notifications about events on the site.
<ul>
<li>Notification about the publication of a new post.</li>
<li>Notification about post updates.</li>
<li>Notification when a user logs in to the site.</li>
<li>Notification about the installation of a new plugin.</li>
<li>Notification about plugin updates.</li>
<li>Notification about the installation of a new theme.</li>
<li>Notification about theme updates.</li>
</ul>
SMS notifications about orders in the WooCommerce plugin. 
* Notification about a new order to the administrator’s phone. 
* Notification about a new order to the client’s phone. 
* Notification about the change of order status to the administrator’s phone. 
* Notification about the change of order status to the client’s phone.
Notifications about events for Contact Form 7.

SMS-Fly

Sending SMS messages using the "SMS-fly" service

You Have a New (BuddyPress) Message vs SMS-Fly