Restoring $_POST-values after $_GET-submit

I'm buildung a pager_query-display with input from a form, that is working correctly with POST-method.

But when navigating through the pager, the submitted data is lost, because the "method" changes.

The form-data is submitted via GET-statements like this:
/site?page=1&formvalue=XXX&op=Action&form_build_id=form-05a475f6160efd619ad635130e4744f5&form_token=6dbac0e894dd93e2fcd9f8b1012dfd97&form_id=form

I understood, that forms api doesn't work wit the GET-method, even if I can change the #method-value to "get".

But how can I access the values submitted in the earlier correct POST-submit? I don't care if someone chance the formvalues in the get-string. It would be enough for me, if I could just restore the values with using the GET-submitted form_build_id, but it doesn't work. I tried somethink like this:
---
if ($_GET['form_build_id']) {
$get_form_build_id = $_GET['form_build_id']; //for now no input-check (TODO)
form_get_cache($get_form_build_id, &$form_state);
}
drupal_get_form('form');

---

Can someone give me a hint, how to get the values from the POST-submit?