I would recommend that you use sessions or maybe someone else would recommend an better way.
Sessions are simple enough. If you are going to be passing the same variable around alot then you should use them.
Code:
session_start(); #required for you to use sessions, recommeded to be the first line of your code
$_SESSION['complete'] = $POST['complete'];
You are passing your HTML post to a PHP session. And that's it. Use this object as you would any other.