You can check that all the variables you require of the user are set (isset($variable)). If so, display your message and hide your form. A redirect will allso work. (php manual)
header("Location: http://www.example.com/");
exit;
Redirect to a page that displays your message.
eg.
Note: headers must be sent before any other HTML(place this code at the top of the page)
<?php
if(isset($var1) && isset($var2) && ...)
{
header("Location: http://www.example.com/");
exit;
}
else
{
...
Form page
...
}