JSFiddle - React, Tailwind, and code Playground

HTML

<select id="mainmenu" style="width:300px">
    <option value>Select from menu</option>
    <option value="one">One</option>
    <option value="two">Two</option>
    <option value="three">Three</option>
</select>
<select id="submenu" style="width:300px">
    <option value>Select from submenu</option>
    <option value="a">A</option>
    <option value="b">B</option>
    <option value="c">C</option>
</select>

CSS

.ui-combobox {
    position: relative;
    display: inline-block;
  }
  .ui-combobox-toggle {
    position: absolute;
    top: 0;
    bottom: 0;
    margin-left: -1px;
    padding: 0;
    /* support: IE7 */
    *height: 1.7em;
    *top: 0.1em;
  }
  .ui-combobox-input {
    margin: 0;
    padding: 0.3em;
  }

JavaScript

$(function(){
    $('select').combobox();
});

$( document ).ready(function() {
    $("#mainmenu").combobox({
            selected: function (event, ui) {
               var selectVal = $('#mainmenu :selected').val();
                if(selectVal=='two'){
                 $('#submenu').next().find('input').focus();
                }
            }
        });
});


/* 
    Combobox widget 
    - taken from http://jqueryui.com/autocomplete/#combobox
    - added support for
      - default option
      - combo uses width of original select
      - autoFocus
    - removed
      - tooltips
      - setting value to "" if invalid (instead sets to default)
*/
(function ($) {
    
        $.widget("ui.combobox", {
            _create: function () {
                var input,
                  that = this,
                  wasOpen = false,
                  select = this.element.hide(),
                  selected = select.children(":selected"),
                  defaultValue = selected.text() || "",
                  wrapper = this.wrapper = $("<span>")
                    .addClass("ui-combobox")
                    .insertAfter(select);

                function removeIfInvalid(element) {
                    var value = $(element).val(),
                      matcher = new RegExp("^" + $.ui.autocomplete.escapeRegex(value) + "$", "i"),
                      valid = false;
                    select.children("option").each(function () {
                        if ($(this).text().match(matcher)) {
                            this.selected = valid = true;
                            return false;
                        }
                    });

                    if (!valid) {
                        // remove invalid value, as it didn't match anything
                        $(element).val(defaultValue);
                        select.val(defaultValue);
                        input.data("ui-autocomplete").term = "";
                    }
                }

            ...