If the member belongs to a group that has a Group Image assigned to it, they will be able to choose (from their profile settings page) to have that Group Image displayed on their profile.
The Group Badge is linked to the group, not to the member.
You can change the Group Image as often as you'd like, and all members within that group will receive the updated Group Image selection option. If you remove a Group Image, then no members in that group will have a Group Image.
Your member only needs to visit their profile settings page and select the new Group Image.
