JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1/themes/base/jquery-ui.css">
<link rel="stylesheet" href="http://github.felixnagel.com/selectmenu/themes/base/jquery.ui.selectmenu.css">
<script src="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.16/jquery-ui.js"></script>
<script src="http://github.felixnagel.com/selectmenu/ui/jquery.ui.selectmenu.js"></script>
<form action="#">
    <div>
        <select id="sel1">
            <option value="">Select a Value</option>
            <option value="A">Option A</option>
            <option value="B">Option B</option>
            <option value="C">Option C</option>
        </select>
    </div>
    <div><label for="chksame">check to make same</label><input type="checkbox" id="chksame"></div>
    <div>
        <select id="sel2">
            <option value="">Does not change display</option>
            <option value="A">Option A</option>
            <option value="B">Option B</option>
            <option value="C">Option C</option>
        </select>
    </div>
</form>

CSS

/* demo styles */
body {font-size: 62.5%; font-family:"Verdana",sans-serif; }
fieldset { border:0; }  
label,select,.ui-select-menu { float: left; margin-right: 10px; }
select { width: 200px; }    
.wrap span.ui-selectmenu-item-header,
.wrap ul.ui-selectmenu-menu li a { text-decoration: underline !important; }

JavaScript

$(function() {

    $('select').selectmenu({
        style: 'popup'
    });

    $('#chksame').click(function() {
        if ($(this).is(':checked')) {
            var selectedValue = $('#sel1').val();
            $('#sel2').val(selectedValue);
            
          //  $('#sel2-button span').text($("#sel2 option[value='" + selectedValue +"']").text());
            
            $('#sel2').selectmenu("value", selectedValue);
            
        }

    });
});