Sometimes, it's better to save an iMessage attachment to your device rather than let it sit in the Message app. If you need to save a photo or video that was sent to you, follow the same instructions as above to locate the attachments in iMessage. Tap 'See All,' then tap on the one you want to save. In the lower-left corner, tap on the share icon. Then, select 'Save image.' You can also share the image among other options. You can do the same thing for any documents that have been sent to you via iMessage.