var $options = $("#myselect > option").clone();

$('#secondSelectId').append($options);

ライブデモ

<select multiple="true" class="multiselect1" name="myselecttsms1">
    <option value="1" rel="0" title="One">One</option>
    <option value="2" rel="1" title="Two">Two</option>            
    <option value="4" rel="3" title="Four">Four</option>
    <option value="5" rel="4" title="Five">Five</option>
    <option value="6" rel="5" title="Six">Six</option>
</select>

<select multiple="true" class="multiselect2" name="myselecttsms2" size="6">

</select>

<button class="add">Add</button>
<button class="addAll">Add All</button>
<button class="remove">Remove</button>
<button class="removeAll">Remove All</button>

jQuery：

$('.add').on('click', function() {
    var options = $('select.multiselect1 option:selected').sort().clone();
    $('select.multiselect2').append(options);
});
$('.addAll').on('click', function() {
    var options = $('select.multiselect1 option').sort().clone();
    $('select.multiselect2').append(options);
});
$('.remove').on('click', function() {
    $('select.multiselect2 option:selected').remove();
});
$('.removeAll').on('click', function() {
    $('select.multiselect2').empty();
});

サンプルワークアウト