How to keep/access copy of original Feed file when using HTTP Fetcher?
I have a simple solution for you but in this time I have not enough time to test it by myself.

First find your importer form_id, then in your custom module add custom submit handler then get URL of uploaded file then save it in where you want with system_retrieve_file(), e.g.:

function yourmodule_form_alter(&amp;form, &amp;$form_state, $form_id){
  if ($form_id == "importer_form_id") {
    $form['actions']['submit']['#submit'][] = 'yourcustom_form_submit_handler';
  }
}

function yourcustom_form_submit_handler($form, $form_state){
  // dpm($form_state['values']);
  // find file url and put it in $url
  // then try to fetch it with system_retrieve_file
  system_retrieve_file($url);
}