How to import image using Feeds which doesn't have a correct file extension?
I managed to solve this by using the feeds tamper module with the following php snippet to save the image and then reference the path on my server.

$checkext = substr($field, -5);

if (strpos($checkext,'.') == false)
{
  $filename = str_replace(".","_",microtime(true)).".jpg";
  $output = "public://field/image/".$filename;
  file_put_contents($output, file_get_contents($field));
  return  $output;
}
else
{
  return $field;
}