Hi
I can only base my answer on my phone, as you didn't mention what kind of phone you have.
I touch on the thumbnail of the pic in the text message, it opens to the larger picture. I have, a "save" option at the top right hand side, once the bigger picture opens. I hit save, and its now in my gallery.
It might be different for you. Once you click on the picture, and if your save option doesn't immediately appear, try touch and hold on the "opened" picture from your message and see if it bring up the option to save it.
Hope this helps!
Chris