how do I stop payment and transfer my iCloud storage and use the one of my family?

I have a monthly subscription to iCloud storage and have about 70gb of data in it. My family member also has a subscription and they just upgraded it to a family plan which would be more than enough to cover my 70gb of data.

I've tried from several different angles and cannot seem to find a way to just switch over to their account and stop paying extra. It appears I have to delete all (but 5gb) my data, stop my plan, wait for it to lapse, and then start on my family member's plan. That cannot be right.

How in the world do I switch over and not lose everything? If it's a family plan and family members cannot join without deleting all their data first, something is not right.