Bernhard Kau

This plugin enables blog admins and editors to manage the notification of incoming comments. As WordPress only has the option to notify on every comment, the email account of the admin may recieve many email each day. Notification is also limited to the admin only, so only the admin user will receive an email for incoming comments.
Using the plugin you can subscribe to a RSS feed that contains even comments that has to be moderated. Every feed entry has the links to delete a comment, mark a comment as spam or approve a comment, if the comment has to be moderated. If a comment has been marked as spam, it will no longer appear in the feed.
A list of all of my plugins can be found on the <a href="http://kau-boys.de/wordpress-plugins?lang=en" title="WordPress Plugins" rel="nofollow ugc">WordPress Plugin page</a> on my blog <a href="http://kau-boys.de" rel="nofollow ugc">kau-boys.de</a>.

Kau-Boy's Comment Notification

This plugin enables blog admins and editors to manage the notification of incoming comments. It offers a special RSS feed with all comments, including …

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Yin Zhongzhen

This simple plugin automatically sends a notification email to commenters when someone replies to their comment. This feature can be enabled automatically by the site admin, or through an opt-in/opt-out checkbox below comment section on frontend.
It’s best to use it with an email-sending plugin like WP Mail SMTP, and with SMTP or transactional email service like SendGrid or Mailgun. Sending from your server via PHPmailer can cause deliverability issues (email notfications caught in spam).
I loved the original plugin <a href="https://wordpress.org/plugins/comment-reply-notification/" rel="ugc">Comment Reply Notification</a> (by @denishua) for its simplicity but it was abandoned and stopped working years ago. So I forked and revived it to work with the latest PHP and WordPress. I also improved some wording, removed unnecessary author links in the email notifications, and also keep it more updated. Credits to Denis who first hacked it 5 years ago, and later Walter for fixing string escapes.
<h4>Features:</h4>
<ul>
<li>Feature modes – disabled, author/admin replies only, automatically, checkbox opt-in.</li>
<li>Edit email notification – subject and message.</li>
<li>[year] shortcode for dynamic year in email templates.</li>
<li>Developer-friendly hook for adding custom shortcodes.</li>
<li>Fixes issue with email notifications for moderated comments.</li>
<li>Can delete plugin options – after deactivation.</li>
</ul>

Comment Reply Email

Commenters can receive email notifications of replies to their comments.

Kau-Boy's Comment Notification vs Comment Reply Email