You will have seen that the Price Group of your inventory lives at the Product Family level of your hierarchy.
So to change the that Price Group you must edit the respective Product Family:
navigate to that Product Family on the inventory manage page.
and then edit the Product Family.
You will then be able to change the Price Group for this PF:
Please note that when looking lower down the hierarchy, e.g. the PL or the Item it will show your Price Group, but you won't be able to edit from these lower levels: