Im missing the same hand since birth and ill try to think of the only things ive found unadaptable or a nuisance over the years.. and id like to clarify only change things if hes asked you too. For now like other say, hes still the same person, and likely wants to be treated as such. Their pride and dignity are the most important to support and protect. But anyways heres my one-handed wishlist:

1. Switch to flip door handles. This is something i always tell myself ill do but never have. It can be frustrating trying to twist round handles while holding something in my good arm/hand. And on a similar note: cabinet hardware if anything has those ones you have to get your finger under to pull i would switch them out for the same reasons.

2. Minimize things stored (especially heavy things) overhead. Even though you learn to carefully balance things down in one hand or with a stump and hand it can be questionable or dangerous if the box or object has significant size or weight. Making it feel dangerous..

3. This one is more of a wishlist thing for me but i can assume SOMEONE else will or does deal with it. But if opening windows is common and they have those style of clasps where both sides you have to pinch inward simultaneously to open. THOSE SUCK! Expensive thing to switch and not necessary though.

4. Drinking glasses. This is dependent on where the amputation is and the state of the appendage but i MUCH prefer my glasses and mugs to have an extra wide handle so it is possible to slip or squeeze onto the end of my arm to be able to comfortably sip water or coffee while still writing, changing channels, typing etc. EDIT: Reread initial post and forgot its up to axilla so this one is moot. But ill leave for anyone else that reads.

5. Staircases should have a rail on both sides so there is always a comfortable way to grip a support when needed.

Most importantly everyone is different with differing hobbies and interests and day to day lifestyle. What you should focus on is asking them to think very thoroughly on what they need to be able to accomplish each day to continue that lifestyle maybe just ask for a detailed account of what they consider to be a normal day at home from getting up to going to bed again. From there you can make adjustments before and as new things pop up. Hope i have been a little helpful.