Private Groups - Not allow comment, re-post, social share by group members

Hi,

We've created private "invite-only" groups and enabled custom field to only allow admin to post in the group. Feature works somewhat. Although group member is unable to post in the share-box (gets an error message that you're not allowed to post), they're able to repost in this group. We believe that should not be allowed as well if we're restricting all share/post permissions for members in such groups. Can this be resolved?

Cheers!