Hey Shamim,

What are your thoughts on this? This seems to get the job done.

   add_filter( 'fep_filter_message_query_sql', 'fep_filter_message_query_sql', 10, 2 );

   /**
     * Allows for the searching of student number on the message list page
     *
     * @param $sql
     * @param $class
     * @return mixed
     */
    function fep_filter_message_query_sql( $sql, $class ) {

        if( isset( $_GET['fep-search'] ) && ! empty( $_GET['fep-search'] ) &&
            preg_match( '/^\d{7}$/', trim( strtolower( $_GET['fep-search'] ) ) )
        ) {

                global $wpdb;

                // Inject DISTINCT cause the join seems to bring duplicate records
                $sql = str_replace( 'SELECT ', 'SELECT DISTINCT ', $sql );

                // Inject the users table join
                $sql = str_replace( ' WHERE', ' INNER JOIN ' . $wpdb->users . ' on adm_fep_messages.mgs_author = ' . $wpdb->users . '.ID WHERE', $sql );

                // Inject for the where on user_login = ?
                $sql = str_replace( ' ORDER BY',' OR ( ' . $wpdb->users . '.user_login = "' . esc_sql( trim( strtolower( $_GET[ 'fep-search' ] ) ) ) . '") ORDER BY', $sql );
        }

        return $sql;
    }