Regarding:

My problem I m having a hard time parsing the string HTML tag and save it in a PHP array.

I suggest that you use an HTML parser, such as simplehtmldom. This will allow you to traverse over HTML DOM just the way you want.

Here is a quick and dirty UL walking script:

<?php
    require_once( "simplehtmldom/simple_html_dom.php" );
    $DOM = file_get_html( "test.htm" );
    $ARR = array( );
    function WalkUL( $ul, &$ar )
    {
        foreach( $ul->children as $li )
        {
            if ( $li->tag != "li" )
            {
                continue;
            }
            $arar = array( );
            foreach( $li->children as $ulul )
            {
                if ( $ulul->tag != "ul" )
                {
                    continue;
                }
                WalkUL( $ulul, $arar );
            }
            $ar[ $li->find( "a", 0 )->plaintext ] = $arar;
        }
    }
    WalkUL( $DOM->find( "ul", 0 ), $ARR );
    print_r( $ARR );
?>

Its output, not exactly as you wanted it but close:

Array
(
    [Folder 1] => Array
        (
            [Child 1.1] => Array
                (
                )
            [Folder 1.1] => Array
                (
                    [Child 1.1.1] => Array
                        (
                        )
                )
            [Folder 1.2] => Array
                (
                    [Child 1.2.1] => Array
                        (
                        )
                    [Child 1.2.2] => Array
                        (
                        )
                )
        )
    [Folder 2] => Array
        (
            [Child 2.1] => Array
                (
                )
            [Child 2.2] => Array
                (
                )
        )
    [Outer Child] => Array
        (
        )
)

Instead of messing with html you should submit the tree data in a more programmer-friendly format.

$( #saveButton ).click(function() {
    var treeData = $.tree.reference($( #sortableTree )).get(undefined,  json );
    var tmp = serializeTree(treeData, 0);
    // now json-encode tmp and submit it
});

function serializeTree(nodes, parent)
{
    var parents = {};
    var childOrder = []
    var childOrders = {};
    for(var i = 0; i < nodes.length; i++)
    {
        var node = nodes[i];
        var id = node.attributes.id.substr(5); // assuming the id looks like  abcd-ID 
        parents[id] = parent;
        childOrder.push(id);
        if(node.children)
        {
            var tmp = serializeTree(node.children, id);
            for(var id in tmp[0])
                parents[id] = tmp[0][id];
            for(var id in tmp[1])
                childOrders[id] = tmp[1][id]
        }
    }

    childOrders[parent] = childOrder;

    return [parents, childOrders];
}

Just for referecence: there s also a jQuery plugin for serializing a HTML DOM Tree of <ol> and <ul> lists: http://www.drakedata.com/serializetree/sampleTree.html - it converts a nested structure of <ol> and <ul> lists to a string which can be used as an associated php array.

If you have a UL that does not contain any href elements (e.g. just plain text nexted ul).. I ve adjusted Salman s simplehtmldom code to work with that:

$DOM = str_get_html( $catshtml );
$ARR = array( );
function WalkUL( $ul, &$ar )
{
    foreach( $ul->children as $li )
    {
        if ( $li->tag != "li" )
        {
            continue;
        }
        $arar = array( );
        foreach( $li->children as $ulul )
        {
            if ( $ulul->tag != "ul" )
            {
                continue;
            }
            WalkUL( $ulul, $arar );
        }
        $ar[ trim(preg_replace("#</?[a-z]+[^>]*>(.+</[a-z]+[^>]*>|)#is","",$li->innertext)) ] = $arar;
    }
}
WalkUL( $DOM->find( "ul", 0 ), $ARR );
echo "<pre>"; print_r( $ARR );