To expand a bit on Peak's post - yes, it is the AMC 4K Committee which handles the NE111 paperwork, scroll and patches now. IIRC, Mike Dickerman is the person who actually handles it. And yes, the AMC Guide for Maine is probably the best source of trail info for the Maine Peaks. That, and a Delorme map book will go a long way. There's a couple of books, and few maps, which are helpful for the ADKs. If you need that info and can't find it using the Search function, post a request.
When I finished them a few years ago, I did the New England 67 first, sent in the paperwork, then did the ADK's plus Hunter & Slide in the Catskills. I submited the paperwork to ADK 46er committee, and then sent in the paperwork to the Northeast 111, which at the time was handled by Priscilla Robertson. Keep track of both the date and time you finished the final ADK, as well as Hunter & Slide. The reason for noting the time is not at all clear to me, but the ADKer's assign you a number, so maybe the number is somehow related to the time? Who knows? But the ADK number is a big deal to some people, so I need to act respectful regarding it.
Be patient when dealing with the AMC 4K committee as they can be very slow to respond. The ADK 46'ers, OTH, are pretty fast, in my experience.
Hope this helps, and good luck to you and your son. The completion of that goal is a big accomplishment, and not too many manage it, especially father and sons.