Look I'm not gonna lie, him going to Hogwarts would be completely stupid and a waste of time.
He is a Member of the Gremory Heiress Peerage, she can literally buy Wizard and Witch Tutors for Harry.
If he goes to Hogwarts it will be super forced imo.
And how did the letter reach Harry, if he no longer lives in the United Kingdom? Or is it that as long as the quill and the book record the magic, no matter where he moves to afterwards, he still has an opening?