Send email notifications via wp_mail when a post is submitted (pending review) then notify the post author that the post has been published.

post_email_notifications.php

<?php
function _pit_pending_post_status( $new_status, $old_status, $post ) {
    $post_author_id = $post->post_author;
    $post_author = get_the_author_meta( 'display_name', $post_author_id );

    $post_date = $post->post_date;
    $post_title = $post->post_title;

    if ( $new_status === 'pending' && $old_status !== 'pending' ) {
        $headers[] = 'Content-Type: text/html; charset=UTF-8';
        $headers[] = 'From: PracticalIT <[email protected]>' . "\r\n";

        $admin_emails = array(
            '[email protected]',
            '[email protected]'
        );
        $subj = $post_title . ' is waiting review';
        $body = '<b>' . $post_title . '</b> post by <em>' . $post_author . '</em>, submitted on <b>' . $post_date .'</b> is waiting review.';
        wp_mail( $admin_emails, $subj, $body, $headers );
    }
}
add_action( 'transition_post_status', '_pit_pending_post_status', 10, 3 );

function _pit_on_publish_pending_post( $post ) {
    $headers[] = 'Content-Type: text/html; charset=UTF-8';
    $headers[] = 'From: PracticalIT <[email protected]>' . "\r\n";

    $post_date = $post->post_date;
    $post_title = $post->post_title;

    $post_author_id = $post->post_author;
    $user_email = get_the_author_meta( 'user_email', $post_author_id );

    $subj = $post_title . 'has been approved';
    $body = 'Your post - <b>' . $post_title . '</b> submitted on <b>' . $post_date .'</b> has been approved.';
    wp_mail( $user_email, $subj, $body, $headers );
}
add_action(  'pending_to_publish',  '_pit_on_publish_pending_post', 10, 1 );