May I know which "share photo" icon you referring to?

It would be good if you can share a screenshot with us, it will help us to better understand which part are you referring to.

I have one site showing this option, and the other is not. So the attached screenshot shows what I'm seeing that I would like to have show on the other site.

Did it show the photos icon If you click the + plus button?

Also, did it show the photos icon on their user profile timeline?

If no, I guess either the group category itself already turned off this upload photo feature or the user does not have permission to upload a photo in the group.

If still can't manage to show it out, you might need to update your site backend and FTP access at your first post so we can better have a check.