Issue: Customer was getting this error message " Changes to the public group membership cannot be saved. you do not have sufficient permission to perform this operation on the object
Finding: Users(owners) who managed groups were put in a universal distribution/security group called grp-groupname. In AD console, the groups were added as managers under the managed by tab. This worked ok in Exchange 2007. However, group owners that are migrated to Exchange 2010 get permission errors trying to add a member to the group via Outlook 2007/2010. Exchange 2010 console now has managed by property beneath newly added group information tab. By so doing, one can't use groups to manage security/distribution group, mail enabled or not. Exchange 2010 console shows the grp-groupname as object not found.
This problem doesn't apply to groups that only 1 owner assigned.
Resolution: While in exchange mgmt console, Add the owners of the group under managed by property of Group information tab. Note that this will upgrade the group to exchange 2010 group. Only Exchange 2010 groups can allow multiple owners of the mailbox. Customers that want multiple owners for a group will need that group upgraded. Another way to upgrade a group is by using this powershell cmdlet. You must do this in exchange 2010 shell
set-distributiongroup -Name -forceupgrade