How to save ul li variables to database – Jquery ajax

i have such an example… From here (http://jsfiddle.net/tpgun6Lz/5/) i have dropdown menu(with images) using ul li (in my example there will be few different menu).
Here is a code – i can add the id to <ul>(but as you will see jquery using class not using id), and data-value to <li> for the purpose of solve problem:

<ul class="prod-gram" id="menu">
    <li class="init" data-value="1"><img src="http://smartangielski.j.pl/img/hej.png" /> Country 1</li>
    <li data-value="2"><img src="http://smartangielski.j.pl/img/hej.png" /> Country 1</li>
    <li data-value="3"><img src="http://smartangielski.j.pl/img/hej.png" /> Country 2</li>
</ul>
<ul class="prod-gram" id="menu2">
    <li class="init" data-value="1"><img src="http://smartangielski.j.pl/img/hej.png" /> Country 1</li>
    <li data-value="2"><img src="http://smartangielski.j.pl/img/hej.png" /> Country 1</li>
    <li data-value="3"><img src="http://smartangielski.j.pl/img/hej.png" /> Country 2</li>
</ul>

and javascript:

<script>
    $(document).ready(function() {
        $(document).on("click", "ul.prod-gram .init", function() {
            $(this).parent().find('li:not(.init)').toggle();
        });
        var allOptions = $("ul.prod-gram").children('li:not(.init)');
        $("ul.prod-gram").on("click", "li:not(.init)", function() {
            allOptions.removeClass('selected');
            $(this).addClass('selected');
            $(this).parent().children('.init').html($(this).html()); // this line colide with ajax
            $(this).parent().find('li:not(.init)').toggle();
        });
    });
</script>

I want to save value ul(id), and value li (data-value) in PHP using jQuery and ajax. I prepare some code but I don’t know how to setup them(I’m not sure about variables setup and ajax):

<script>
    $('#menu').click(function(){
        var liValue = $(this).closest('li').attr('data-value');
        var ulId = $(this).closest('ul').attr('id');
        jQuery.ajax({
            type: "POST",
            url: 'humourvalue.php',
            data:{ul: ulId, li: liValue},
            success: function(data) {
                $("#menu").html(data); // i tried to change datatype but then i cant send them to php
            }
        });
    });
</script>

and file humourvalue.php

<?php
    require_once 'includes/config.php';

    if(isset($_SESSION['user_id'])) {
        if ($userID === null) {
            $userID = $_SESSION['user_id'];
        }

        $userID = intval($userID);
        $ulId = $db->$_POST['ul'])));
        $liValue = $db->$_POST['li'])));
        $result = $db->query("UPDATE `users` SELECT `opts`='".($ulId)."' WHERE id=".($userID));
    }

?>

I’m not sure if this topic will be helpful to get data from database: how to get data to html <ul> <li> </li> </ul> list from mysql database with php

I need to focus first how to save variables in database. Please help me with this, course it makes me crazy.

——————UPDATE————
Now i undertand – the javascript code colide with ajax call, couse we have

$(this).parent().children('.init').html($(this).html());

in javascript and in ajax we have

success: function(data) {
         $("#menu").html(data);

Can anyone have some idea how to fix it?