How much time between the news and the move?

I think it would be stipulated in the will.

If the old house is in an area of England that sees cold winters, someone might have it in mind that they need to get out there before the pipes freeze and so on.

Maybe you can use those sorts of things to get the timing you need.

Not what you asked, but why complicate the issue by making it a condition of the bequest that he has to go and live there? How long is he expected to live there? Till he dies? What if the family were perfectly happy where they were and didn't want to move?

Anybody would be thrilled to discover out of the blue they were the owner of a mansion in the UK and would surely do what anyone would do - take a holiday and go over to check it out with the family. He can always sell it in a few years time, and the bogle story will be finished long before then. Surely all you need is for him and his family to be at the house for the duration of the bogle story.

The time element can be whatever you choose.

Allow for appropriate travel arrangements and finalising whatever has to be finalised. Three months, whatever - I doubt anyone is going to question the time element at all but if he's really going to be packing up everything and leaving permanently the time may be a tad longer than if he weren't, depending upon whatever has to be done.

How long is a piece of string? Unless the will specifies a time period - one calendar year from grant of probate perhaps - then he can take as long as he needs. It is clearly unreasonable to expect him to take up residence within a month. There are practicalities to consider - kids in school, renting/selling out current residence, arranging residency permits (not at all straightforward - Google "can a US citizen live in the UK") which all take time.

Particularly, funding all this. Unless the will also gave the heir a giant pile of money, to say 'you must live in the house in England' is more of a burden than a gift. How are they supposed to support themselves, if nothing else?
Other than that, leaving their US home (and all the stuff Waylander said) to move to a foriegn country in a house that may or may not be a money pit, sounds a little foolish. It's the kind of situation that might leave the heir looking for a lawyer to figure out how to get him out of the deal.

And, whatever the will intended, if the fantasy part was something like 'If a member of the family doesn't live here, the bogles will claim the countryside', weeeell, that's not exactly an inducement, is it? Who wants to raise their children in a bogle-infested old place? It's not like they're being promised Downton Abbey and money to boot.

Not to brag, but I moved me and two kids to Malaysia in 13 days, which included rehoming the cat, putting the house on the rental market and - worst thing ever - getting the kids and me vaxxed before we left. Also letters of introduction from their schools.

I was hoping never to think about that again, but there you go.

If you want to root this fantasy firmly in the child's POV and focus on the fantasy, not realism, it probably doesn't matter than from the adult perspective the whole setup sounds fishy and the logistical challenges (inc but not limited to arranging for visas, work and residency permits, jobs, disposing of their old house, etc.) are very complex and don't have a guaranteed good outcome. You can handwave most of the adult issues -- kids don't know, don't understand, don't care about a lot of things that keep grownups awake at night, they have their own priorities & concerns. Push the logistical details into the background.

That said, if you are aiming for more realism than fantasy, you'll need to deal with all the issues that waylander and frimble3 mentioned. Relocating a whole family long-term from Missouri to England is a complicated endeavor, and the shorter the timeframe the more difficult & stressful for everyone.

Anywhere from tomorrow until never at all. Write the timeline you need with the conditions you need to achieve it.

Jeff