Problem: SharePoint group owner cannot add user! group owner gets access denied.
Root cause: It’s a common misconception that group owners get access automatically, as you are made the owner of the group! Just because you made someone “Group Owner” doesn’t mean they get access to the site! They can’t access the site until you grant permission to that group owner user.
And its also true that group owners can’t add/remove users unless they have “Manage Permissions” rights!
So, the solution is to grant permission to the user by adding them to the appropriate SharePoint Group or to the Active Directory group, which has access to the site already! This gets them access to the site. And to add other users to the group, the group owner should have a permission level consisting of permission “Manage Permission” (such as “Full Control”).