Can I move a shared album in Photostream to My albums?

I would think this paragraph from the article linked above explains.

”The photos in My Photo Stream are already stored on at least one of your devices, so as long as you have the device with your originals, you won’t lose any photos as part of this process. If a photo you want isn't already in your library on a particular iPhone, iPad, or Mac, make sure that you save it to your library on that device.”