If I understand it right, the server on the external URL should convert the file you're uploading and return a converted version of the file. Thus, this converted version would be contained in the body of the server's response. So it's not enough to simply check the status but you have to get the response itself.
You can achieve that by using client.execute()
instead of client.executeMethod()
about like so:
HttpResponse response = client.execute(filePost);
InputStream is = response.getEntity().getContent();
Now you can read the converted data from the input stream is
and proceed as you like (e.g. save to disk etc.)