Использование может исключать .asset-paid-li
с использованием селектора :not()
.Также используйте .clone()
вместо получения HTML элементов.
$("input:checkbox").click(function(){
if (this.checked)
$("ul#mosaic li:not(.asset-paid-li)").clone().appendTo("ul#assetSelectedList");
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<input type="checkbox" name="thing" value="valuable" id="thing1">
<ul id="mosaic" class="clearfix list">
<li class="clearfix asset-free-li">Asset Free</li>
<li class="clearfix asset-free-li">Asset Free</li>
<li class="clearfix asset-paid-li">ASSET PAID</li>
<li class="clearfix asset-free-li">Asset Free</li>
<li class="clearfix asset-free-li">Asset Free</li>
<li class="clearfix asset-paid-li">ASSET PAID</li>
<li class="clearfix asset-free-li">Asset Free</li>
<li class="clearfix asset-free-li">Asset Free</li>
</ul>
<ul id="assetSelectedList" class="clearfix list"></ul>