JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="//code.jquery.com/ui/1.12.1/themes/base/jquery-ui.css">
<script src="//code.jquery.com/ui/1.12.1/jquery-ui.js"></script>
<div id="notheld-container">
<h3>Properties Not Held by <em>Client</em></h3>
<ul id="notheld" class="connectedSortable"> 
 
</ul>
</div>
<div id="held-container">
<h3>Current Holdings</h3>
<ul id="held" class="connectedSortable ui-sortable"> 

<li class="ui-state-highlight ui-sortable-handle" id="12">Farragut (12)</li><li class="ui-state-highlight ui-sortable-handle" id="1010" style="">King Street (1010)</li>
<li class="ui-state-highlight ui-sortable-handle" id="07">Annandale (07)</li>
<li class="ui-state-highlight ui-sortable-handle" id="13">Aquahart (13)</li>
</ul>
</div>

CSS

#held, #notheld {
    border: 1px solid #eee;
    width: 272px;
    min-height: 20px;
    list-style-type: none;
    margin: 0;
    padding: 5px 0 0 0;
    float: left;
    margin-right: 10px;
  }

  #held li, #notheld li {
    margin: 0 5px 5px 5px;
    padding: 5px;
    font-size: 1.2em;
    width: 250px;
	cursor:move;
  }

  
  #notheld li {
    float: left;
    clear: none;
    display: inline-block;
	}
	
	div#notheld-container, div#held-container {
		width: 300px;
    float:left;
	}

JavaScript

$( "#held, #notheld" ).sortable({
	  connectWith: ".connectedSortable",
	}).disableSelection();
	
	$('#held li').on('dblclick', function() {
		var litem = $(this).clone();
		litem.appendTo($('#notheld'));
		$(this).remove();
		update_holding(litem.attr('id'), 'remove');
		$( "#held, #notheld" ).sortable( "refresh" );
	  });
	  
	  // dropped
	  $('#held').on('sortreceive', function(event, ui) {
		update_holding(ui.item.attr('id'), 'add');
	  });
	  
	  $('#notheld li').on('dblclick', function() {
		var litem = $(this).clone();
		litem.appendTo($('#held'));
		$(this).remove();
		update_holding(litem.attr('id'), 'add');
		$( "#held, #notheld" ).sortable( "refresh" );
	  });
	  
	  // dropped
	  $('#notheld').on('sortreceive', function(event, ui) {
		update_holding(ui.item.attr('id'), 'remove');
	  });
	  
	  function update_holding(EntityNumber, action) {
		  // ajax here
	  }