Currently, enabling all members of a group to edit all content shared with the group requires that the "update capabilities" option be set upon group creation, (which normally is an admin-only or custom role privilege), after which it can not be changed. Likewise, an existing group can not have this option enabled. If one desires to change this option, a new group must be created with the desired setting.
This option should be toggleable at any time, rather than being set in stone at group creation (and doing so should be a non-admin privilege).