Your partner may prefer different pronoun than 'he'.

Just ask them. And give it time, both to learn and to adapt. Both of you. Nothing is set in stone and no big change happens fast.
I am one of the 'lucky' girls. I lost my hair. What I wear I call manes, but in stores they will respond better to the word 'wig'. I guess it depends on your budget greatly what you will get.
Some cis women (born as what doc calls girls) go bald too. Go where they are going. Ask your GP. I didn't find a good place for myself until I asked my GP. They helped me find a good-ish place.

Probably also someone from your area can recommend store that will take you in, talk you through the options and then you can come again here to ask before you make final decision. In either case I recommend cool-off period before getting manes.

Short demonstration by letting your partner actually wear the mane would be great too. I am not in the US, so may not count that all stores that are remotely serious let me wear manes first.
What I know... for full day wear every day, you may strongly prefer having two good manes. So you can swap them every week. Or have backup in case something goes wrong. Since those are expensive, and since I am not really invisible, I also use cheaper ones for dirty work and just for sleep. Also, if you are not 100% sure, do take just one and see how that goes. If it is all well, take another one in a week or two... in the start they won't be worn full days I suppose.
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Do take care to get the right mane's diameter for head, or your partner would get strong marks over the head which is probably not what either of you wants. Cheaper manes will leave some marks that should disappear within a hour if size is right; *ymmv* warning though! Those scratches may be avoided with use of pads made for that purpose. Well, also my best manes leave a single, subtle not irritated stripe above the forehead after full day. It is ymmv what is safe and comfortable. Best sorted out with pro and if you can get to test manes for free, go there and test them.
Just in case... by full day I mean anything between the two:
* All time spent outdoors
* All time spent when not in bed or shower, and such
Another important thing, get manes that match your partner's head/face shape and skin tone. Some manes are gorgeous but they make me look horrible because they don't match my face and head. That is why trying it on before purchase. About the skin tone, you may want to actually dye the manes, so shape gains priority big time. I never dyed my manes, but it is probably my loss. Do ask people in the store to do this for you, manes may require different products than hair of those lucky to have it.
Oh, the last but not least. Don't let them sell you damaged wares. Have a careful look and touch. Don't buy story if it doesn't add up. If it doesn't feel right, it probably isn't. Don't buy mane if it doesn't look and feel good on the person who will wear it. End of story.
P.S.
As the 'funny' part of this post, I will tell story of one store that is very well supplied, but their culture and customers is a bit off. This store mishandled one of my orders, perhaps treating me as a fetishist who won't come to pick up. I chased them for it until I gave up after a few BS stories. Go figure. Also, when I was there last time, some oldster tried to touch me and was talking dirty to me. WTF. I am glad I found an acceptable place via my GP. First time they took me some deposit to make sure I come back, when I told them I found them through the GP they wanted to return it. After that never got asked for a deposit by them.