I’m glad to see @Josh post a James Randi video. The JREF prize would be very suitable for testing this person’s claim.
In fact, inspired by Randi, I sometimes offer emails I receive with people making such claims to pay their airfare if they would allow me to administer a test with a group of indifferent scientists, members of the public and a panel of the claimant’s choosing.
I don’t think you’d need to give the claimant a difficult programming book. Even the simplest Dr. Suess book would make for a suitable test.
It would also be interesting to have a bonus prize for naming the colors in whichever Suess book was used for the test.
But I think the way to do it would be to take it very seriously. For example, you could arrange for a local bookstore to choose the book from that day’s newest deliveries. First, another employee would hide 10 books in 10 paper bags. Then someone would choose the book, then they would deliver it to the testing location. (Which could be the bookstore itself.)
Only after all of the witnesses had arrived, would the book be revealed to the claimant. No one else would receive a copy until after the memorization and recitation in order to prevent any kind of morse code or other devices sending signals to the claimant. The recitation should also be done with some kind of visual blocking to prevent any kind of sign language from spectators, etc.
Then, as I believe I’ve seen them do with pi demonstrations, the test would be conducted by having a computer randomly select 15 or so pages from the book, i.e. pages 17, 231, 342, etc.
This kind of selection would make the test fair, random and also cut down on the amount of time people have to listen to the recitation. Then again, why wouldn’t this person want to also go for gold and just recite the whole thing if they can do it? You never know: they might also get the gig as a narrator for the audiobook. 
Somewhat related, I met a guy before the lockdowns on the street who saw me rereading The Art of Memory.
He told me he has superior autobiographical memory. I asked, “You mean like Jill Price?”
He didn’t know who she was.
A few minutes later, I asked him for the name of the person with superior memory I just mentioned. He did not know.
This is nothing special on my part, but I’m pretty confident when I see him again I’ll get his name, the name of his dog and the name of his brother correct, or at least in the ballpark. I actually see him around a fair amount and call him by name, but have yet to hear him use mine, even though I’ve mentioned it.
Call me crazy, but I’m much more impressed by the humble, everyday uses of mnemonics, such as remembering the names of the people in your neighborhood. I was on a call with a company the other day and “Bonnie” sounded blown away that I remembered her name when I said goodbye. Just something as simple as that touches lives and makes everything so much greater.