wpml_ls_filter.php

<?php
/**
 * Filter the URL to check if there is query string
 * and attach the query string to WPML URL as well.
 */
add_filter( 'icl_ls_languages', 'my_ls_filter' );
function my_ls_filter($languages) {
    global $icl_adjust_id_url_filter_off;

    if( $_SERVER[ 'QUERY_STRING' ] ){
        if( strpos( basename( $_SERVER[ 'REQUEST_URI' ] ), $_SERVER[ 'QUERY_STRING' ] ) !== false ){
            foreach( $languages as $lang_code => $language ){
                if( is_post_type_archive() ) {

                    $query_string = $_SERVER['QUERY_STRING'];
                    $archived_taxonomy = get_queried_object();
                    $archived_post_type = get_post_type();

                    if( isset( $archived_taxonomy->slug ) ) {
                        $orig_flag_value = $icl_adjust_id_url_filter_off;
                        $icl_adjust_id_url_filter_off = true;
                        $translated_term = get_term( apply_filters( 'wpml_object_id', $archived_taxonomy->term_id, $archived_taxonomy->taxonomy, false, $lang_code ), $archived_taxonomy->taxonomy );
                        $icl_adjust_id_url_filter_off = $orig_flag_value;

                        $query_string = str_replace($archived_taxonomy->taxonomy.'='.$archived_taxonomy->slug, $translated_term->taxonomy.'='.$translated_term->slug, $_SERVER["QUERY_STRING"]);
                    }

                    $languages[ $lang_code ]['url'] = apply_filters( 'wpml_permalink', get_post_type_archive_link( $archived_post_type ), $lang_code ) . '?' . $query_string;

                } else {
                    $languages[ $lang_code ]['url'] = $languages[ $lang_code ]['url'] . '?' . $_SERVER["QUERY_STRING"];
                }
            }
        }
    }
    return $languages;
}