在同一页面上带有ajax帖子的Jquery自动完成小部件

I can't find the issue with my code. On the second page (page2.php) the variable $productid is not there (is null). UPDATE: I forgot to mention I have session_start(); at the beginning of both page1.php and page2.php.

On the first page ex: page1.php I have this:

$(function() {
    $( "#product" ).autocomplete({
        source: 'searchproduct.php',
        select: function (event, ui) {
            var lbl = ui.item.label;
            var value = ui.item.value;
           //store in session
             $.ajax({
                    type: "POST",
                    url: 'page1.php',
                    data: { value : value },
                    success: function(data)
                    {
                        $('#productform input[name="jProductID"]').val(value);
                        $("#productform").submit();
                    }
                });

        }
    });
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
<link rel="stylesheet" href="http://code.jquery.com/ui/1.10.3/themes/smoothness/jquery-ui.css" />
<script src="http://code.jquery.com/ui/1.10.3/jquery-ui.js"></script>

<?php
$productid = $_POST['jProductID'];
$_SESSION['Sproductid'] = $productid;
?>

<form method="post" action="page2.php" id="productform">
 <input type="hidden" name="jProductID" value="productID" />
<label for="product">Produs: </label>
<input id="product" name="productid" id="productid">
<input type="submit" value="Adauga">
</form>

On the second page ex: page2.php I have this:

$productid = $_SESSION['Sproductid'];
echo $productid;

Note: I'm very new to both php and javascript so any advice will be more than appreciated.

</div>

Solved, the code is correct, I was having an error in other part of my code, all the code I posted was inside an if(isset($_GET['...'])) {} wich was returning false. Thank you for your answers.

Just to be sure I replaced

<?php
$productid = $_POST['jProductID'];
$_SESSION['Sproductid'] = $productid;
?>

With

<?php
$productid = $_POST['value'];
$_SESSION['Sproductid'] = $productid;
?>

And I removed the

<input type="hidden" name="jProductID" value="productID" />

And the

$('#productform input[name="jProductID"]').val(value);