add first name, last name, and email to back-end WP user search

admin-user-search.php

<?php
add_action ( 'pre_user_query', 'rkv_user_search' );

function rkv_user_search($wp_user_query) {
        if(false === strpos($wp_user_query->query_where, '@') && !empty($_GET["s"])) {

            global $wpdb;

            $uids       = array();

            $iusib_add  = '';
            // the escaped query string
            $qstr       = mysql_real_escape_string($_GET["s"]);

            $usermeta_affected_ids = $wpdb->get_results("
                SELECT DISTINCT user_id
                FROM $wpdb->usermeta
                WHERE (meta_key='first_name' OR meta_key='last_name'".$iusib_add.")
                AND LOWER(meta_value) LIKE '%".$qstr."%'
                ");

            foreach($usermeta_affected_ids as $maf) {
                array_push($uids,$maf->user_id);
            }

            $users_affected_ids = $wpdb->get_results("
                SELECT DISTINCT ID FROM $wpdb->users
                WHERE LOWER(user_nicename)
                LIKE '%".$qstr."%'
                OR LOWER(user_email)
                LIKE '%".$qstr."%'
                ");

            foreach($users_affected_ids as $maf) {
                if(!in_array($maf->ID,$uids)) {
                    array_push($uids,$maf->ID);
                }
            }

            $id_string = implode(",",$uids);

            $wp_user_query->query_where = str_replace("user_nicename LIKE '%".$qstr."%'", "ID IN(".$id_string.")", $wp_user_query->query_where);
        }
        return $wp_user_query;
    }