When I get a picture in Messages, I just touch and hold the photo, and a window opens with the option to save. When I tap SAVE, it saves in camera roll.
Apple tips says to tap the i, the Details button, touch and hold a photo, then tap More. Select additional photos, then tap Save Images. They’re saved to your Camera Roll.
Try both methods to save a photo and see which one you prefer.
Click HERE for the full tip