Currently there is no way to change a Group's permissions to allow members to edit group items after the group is created. Why? Sometimes business needs change. Right now, we have to create a new group, set the edit privileges on creation, then move all the users over to the new group, and delete the old group.
The simple solution is just make this a setting we can edit after the group is created.
https://community.esri.com/thread/202469-give-someone-else-privileges-to-save-my-web-map-in-portalon...