Here are four ways to share a story map:
1) share the URL in the URL bar
2) search for the story map using the id number in the URL or search for the title (if using the title check that the author is the same). Once you have found it open the item details and select share. You can share with a group that you both belong to. (Note it is possible to invite people to an org with a customized role so they can only view material.)
3) some templates have options in the story map to share via social media
4) in GeoNet there is a way to share items. I believe you use the ! But will check on this
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