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Share option does not appear on activities that are generated by user itself. Which makes sense since that function on activities of other users allows user to share activities of others on its own wall/timeline.
But, there should be option to Share our own posts/activities on other social networks like option for individual photos. Same pop-up should be used. Maybe use different icon like this one:
www.iconfinder.com/icons/211886/share_icon#size=128
for share button on our own posts.
Also, Share option on photos should not be "hidden" in Options menu but moved outside and placed besides Like button.