add_action( 'publish_post', 'fep_cus_user_publish_send_messaage', 10, 2 );

function fep_cus_user_publish_send_messaage( $ID, $post ){

    if ( ! function_exists( 'fep_send_message' ) )
    return;
    $message = [];

    $message['message_to_id'] = $post->post_author; // Post author ID.
    $name = get_the_author_meta( 'display_name', $post->post_author );
    $title = $post->post_title;
    $permalink = get_permalink( $ID );
    $message['message_title'] = sprintf( 'Published: %s', $title );
    $message['message_content'] = sprintf ('Congratulations, %s! Your article “%s” has been published.' . 'nn', $name, $title );
    $message['message_content'] .= sprintf( 'View: %s', $permalink );
    $override = array('post_author' => 1);//change with message sender id


    // Send message
    fep_send_message( $message, $override );
}