AleksHr

If you don’t check your admin panel very often when installing WordPress (perhaps because you prefer to use remote publishing) or want to make sure 
that your clients ‘ WordPress installations are updated, then this plugin is for you. You don’t need to regularly log in to your admin panel, 
subscribe to an RSS feed, or do anything other than install this plugin to receive notifications when WordPress updates, plugins, and themes are released to Telegram messenger.
All you have to do is install the telegram Update Notifier and forget about it until you get a message about the required updates.
To change the Update Notifier Telegram settings, go to the Update Notifier Telegram section in the main settings menu. From there, you can add a unique telegram ID 
that you need to get by writing to the Telegram bot (https://t.me/update_notifier_telegram_bot) . You can also activate update notifications for themes and plugins.

Update Notifier Telegram

Sends notifications to the administrator in Telegram if a new version of WordPress is available. You can also send notifications about available plugi …

Jon Tejnung

This plugin will give you three alternatives for managing your WordPress updates:
<ul>
<li>Update automatically – This updates WordPress/themes/plugins automatically and sends an email to the site admin when an update has been performed.</li>
<li>Update automatically (no email) – Same as the first alternative, but without the email.</li>
<li>Inform about updates once a week – This will send an email to the admin once a week if there are anything that can be updated.</li>
</ul>
Notice that only plugins/themes that resides in the WordPress 
repository will be updated/informed about.
The plugin has not been tested and is not primarily made for multi site-installations.

Simple Automatic Updates

Activate automatic updates or weekly notifications for the site.

Update Notifier Telegram vs Simple Automatic Updates