Saving photos from Photo Stream to Camera Roll

I am trying to move photos from a shared Photo Stream to my Camera Roll on my iPhone, and then have these moved photos appear in My Photo Stream on my Mac. I did this by tapping the send to icon, then selecting Save to Camera Roll. The photos then appears my the Camera Roll on my iPhone, but do not appear in My Photo Stream on my Mac.

Other photos I take with my iPhone are added to My Photo Stream on my Mac.

I have turned off (unchecked) Shared Photo Streams one my Mac (System Preferences > iCloud > Options)