I created a person's profile and invited them to join Geni. They logged in, looked around, and are no longer interested. They aren't doing anything and it's been a long time since they last logged in. When clicking "Inactive Manager", the management of that profile is not transferred to anyone, and the following message is displayed: "This user does not manage any profiles."
How can I reclaim the administration of that profile?
You cannot take over management of a user's profile once they have set a password. If this person is truly not interested, you may suggest to them that they do one of the following:
You can use the Actions menu te become the profile manager it that case
Can you elaborate? How do I do that? Because when reporting an inactive administrator through there, that exact message is shown.
use manager options from the actions menu and add yourself as a manager.
Please show me visually or provide step-by-step instructions on what to click. You are probably talking about a simple thing that isn't working in this case.
You will have to provide a link to the profile for me to do that.
I mean to visually indicate what to click here when there is nothing in this menu that helps recover administrator rights, since the user is not interested in filling out and creating a family tree. Because there is nothing in this menu that would help with that. 
Thanks for the link. It seems the choice is missing from the menu. I will open a ticket for it.