If you received a photo or video as an attachment to a text message, you can save it on your phone. In the message, just touch and hold the attachment to save it. For some attachments, you must touch and hold the blank space beside the attachment.
To view the saved photo or video:
If you do not save a photo or video from a message, it is kept within the message only. So, if you delete the message, you also delete the attachment. (You can try to recover recently deleted messages.)