The OG Access Admins module allows to restrict permissions to change audience/visibility of posts belonging to a group to only administrators of this group.
D7: This module is not necessary in Drupal 7 (D7) since OG natively provides management of permissions for any field (including og audience).
This feature to restrict access control to group admins only seems to have been very often requested in og issues, see for eg.or . The OG Access Admins module provides a solution for this.
By default, with Organic groups, you can configure that visibility of posts to be chosen by author/editor using a checkbox on the posting form. The OG Access Admins module enhances this setup by allowing only group administrators to change this visibility. To put it another way, ordinary (non-admin) members of a group cannot change a private post to be public, nor change a public post to be private, only group admins can do this.
Also, by default with Organic groups, a post that does not belong to any group is automatically set to be public. Therefore, another outcome of the OG Access Admins module, is that only group admins are allowed to change the audience of a post regarding the group(s) they are admins of. This means that ordinary (non-admins) members of a group do not see audience option for this group when editing a node. Of course, for node creation, every members of a group can post in this group.
Note that this means that even if Audience has been set up (in Organic groups configuration) to be optional, every author (but node admins and og admins) has to choose at least one group when creating a node.
Also, this module implies that members of a group, even this group admins, cannot share a post belonging to this group with another group if they are not administrator of this latest group. Conversely, an administrator of a group can pull a post from another group he is member of.