When you share a story or an album on Famicity you have access permissions to the beginning of each form in the "Share with." area.
Clicking in this field, a list of choices will appear. You can then choose which one of your groups will have access to your publication:
(1) In this section, you can add your family or groups with whom you want to share your publication.
(2) Here you can add your family or groups with whom you do not want to share your publication. This is useful when you want to share with a group, but you want to exclude one person from the group.
Once completed, confirm! Nearby you added in the "I want to share" will then have access to your publication.