You would have to use a macro to save the animated gif. Here is a sample
macro. (You have to open [not preview] the message in question.)
Sub SaveAttachment()
Dim objCurrentItem As Outlook.MailItem
Dim colAttachments As Outlook.Attachments
Dim objAttachment As Outlook.Attachment
Set objCurrentItem = Application.ActiveInspector.CurrentItem
Set colAttachments = objCurrentItem.Attachments
For Each objAttachment In colAttachments
objAttachment.SaveAsFile ("C:\" & objAttachment.FileName)
Next
Set objAttachment = Nothing
Set colAttachments = Nothing
objCurrentItem.Close (olDiscard)
Set objCurrentItem = Nothing
End Sub