Add Facebook Profile Picture to an email signature

Question

I'm trying to make an email signature using HTML for someone. What she wants is to automatically pull out her profile pic in Facebook. So every time she changes her picture in Facebook, she doesn't need to change it in her email signature.

After researching, I found out that I can use http://graph.facebook.com/username/picture to get her picture in Facebook. I have tried using http://graph.facebook.com a couple of weeks ago and it's working but now it's not. Here is the result after trying http://graph.facebook.com/username/picture

{
   "error": {
      "message": "(#803) Some of the aliases you requested do not exist: username",
      "type": "OAuthException",
      "code": 803
   }
}

So I googled again and saw this graph.facebook.com/username does not work

So my question, is there an alternative besides http://graph.facebook.com/username/picture?