I'm absolutely no expert, but try pressing and holding the pix. That's how I managed to save my text pix.
Hopefully someone will come in who knows exactly what to do.
You got me pointed in the right direction, mrs pugs. But I had to do it at the right time, which was viewing all messages from that sender, rather than after having pulled up that photo. (Don't know if that made sense.)
When viewing messages from that sender, the photo shows up small. I can click on it which opens up Gallery and the photo is displayed without anything else on the screen. At that point I have no menu options; I can only exit the photo.
But while seeing the thumbnail of the photo in the list of messages I could touch and hold the thumbnail, at which point a menu comes up offering a few options, one of which is "Copy attached to SD card". After I did that I could go to Gallery (from the home screen or from applications, NOT from within Messaging), view the photo and set it as a contact photo.
mrs pugs, you probably didn't need me to explain that, but I put it here in case anyone else is looking for details.
Thank you for your response. As I said, you got me pointed in the right direction.
-boster