on the page where your form is submitting do something like this
session_start();
$_SESSION['data'] = $_POST['data'];
$_SESSION['data_another'] = $_POST['data_another'];
and than you can access those session variables any where like this
session_start(); // this should be at the top of the page before any html load
<input type="text" name="name" value="<?php echo $_SESSION['data'];?>"/>
refresh your page on success call like this
$.ajax({
type: "POST",
url: "yourfile.php",
data: 'data="+ data,
success: function(){
location.reload();
}
});