The easiest solution would be to ask the sender to send it to you as an attachment. You should be able to save it to disk and then it should work if you open it with the right program (IE for animated gif, if that's what it is).
If you see an attachment symbol with the email as it is now, save the attachment (File>Save Attachments in Outlook Express, could be something else in MS Outlook, but you don't tell what email program you use).
Saving embedded pictures can be a problem. And your experience shows that that's certainly the case when they are animated.
Would anyone know how to save an action picture from an e-mail. When I save it by copying the picture the action stops and I only have a picture. How do I retain the action or motion.