. . .
      <? if ($images_res = getAllImages(111)) { ?>
            <div id="img1" class="cycle-slideshow"
                 data-cycle-fx="scrollHorz"
                 data-cycle-timeout="0"
                 data-cycle-prev="#prev"
                 data-cycle-next="#next">
                <? foreach ($images_res as $images_res_key) { ?>
                    <img class="img1" style="height: 140px !important; width: auto;"
                         src="<?= $images_res_key['url'] . 'thumb/' . $images_res_key['name'] ?>" alt=""
                         id="<?= $images_res_key['id'] ?>"/>
                <? } ?>
            </div>
            <div class="center">
                <a href=# id="prev" style="color: #0d88c1">Prev</a>
                <? if ($galleries_list = galleries_list(36)) { ?>
                    <select id="group1" name="group1">
                        <? foreach ($galleries_list as $list) { ?>
                            <option value="<?= $list['id'] ?>"><?= $list['name_en'] ?></option>
                        <? } ?>
                    </select>
                <? } ?>
                <a href=# id="next" style="color: #0d88c1">Next</a>
            </div>
        <? } ?>
. . .
<script>
    $("#img1").cycle({
        timeout: 0,
        fx: 'fade',
        next: '#next',
        prev: '#prev'
    });
. . .
</script>

...
$("#group1").change(function () {
            var id = $("#group1").val();
            $('img.img1').remove();
            $("#img1").cycle('reinit');
            $.ajax({
                type: 'POST',
                url: 'galleries',
                data: 'id=' + id,
                success: function (data) {
                    $.each(data, function () {
                        $('div#img1').append('<img style="height: 140px !important; width: auto; " class="img1" src="' + this.url + this.name + '"/>');
                    });
                    $("#img1").cycle({
                        timeout: 0,
                        fx: 'fade',
                        next: '#next',
                        prev: '#prev'
                    });
                    $("#img1").cycle('reinit');
                }
            });
        });
...

$("#img1").cycle({
                        timeout: 0,
                        fx: 'fade',
                        next: '#next',
                        prev: '#prev'
                    });