Benjamin Berg commented:
Alright, @averi installed a new plugin which allows proper notifications.
Note that it requires manual configuration. To do so, go to Notifications -> Add New.
There, I used the following settings:
Notifications For: New Comment Awaiting Moderation (under Posts)
Email Formatting: HTML (if you want to use the moderation quick links)
Send To: Administrator
Subject: WP Moderation: [post_title]
Content:
A new comment by [comment_author] <[comment_author_email]> has been posted.
<a href="">Go to website for moderation</a>; quick links: [comment_moderation_approve], [comment_moderation_spam] [comment_moderation_delete]
Full content:
[comment_content]If you dislike HTML email, then I recommend the simplified content (as some of shortcodes insert HTML):
A new comment by [comment_author] <[comment_author_email]> has been posted.
Moderation: [comment_moderation_link]
Full content:
[comment_content]