You should be able to use one of the webform hooks to pass $_GET values via redirect.
function YOURMODULE_webform_submission_insert($node, $submission) {
if ($node->nid == XXX){
// Grab the values we need and create our get url parameter string.
$queryString = 'f1=' . $submission['value']['myfield'] . '&f2=' . $submission['value']['myfield2'] . '&f3=' . $submission['value']['myfield2'];
drupal_goto('PATH/TO/FORM', $queryString);
}
}
Or you can use a hook_form_alter for that form, add a new submit callback, and in the new function set the form's #redirect with the same syntax.
$queryString = $form_state['value']['myfield'] . '&f2=' . $form_state['value']['myfield2'] . '&f3=' . $form_state['value']['myfield2'];
$form['#redirect'] = array('PATH/TO/FORM', $queryString);
Then in your custom form, check for the $_GET values, and set them as the defaults to the appropriate fields, if they exist.