As said above, if you’re the “gun guy” of the family and hand your brother a shotgun with a short barrel, he’s not gonna think twice about it until he gets pulled over for speeding or something and gets arrested for the unregistered SBS and becomes a felon. 18” minimum for shotguns.
Anyway, on to how to actually shorten a barrel. I would generally advise against just cutting down a longer barrel because you lose the ability to use chokes (ie the gun becomes cylinder only) and you have the issue with reattaching the bead. Also, as mentioned above, if you have a ribbed barrel you usually want to cut at the end of the rib (so that the bead is supported) which limits your options as far as where you can cut.
CDNN occasionally has advertisements for 870 barrels for less than $100, so you might want to see if they have any in stock. I don’t know anything about them so I can’t really endorse them, but worth a look.
Finally, if you do decide to cut a barrel down, find someone with a metal lathe and have them cut the barrel down properly. While concentricity is not quite as important for a shotgun as it is for say, threading a rifle barrel, a lathe is the proper tool for the job. As a bonus, they will probably be able to cut the barrel for chokes at the same time. Be prepared to pay handsomely for this though. Shop rates are pretty high and this would almost assuredly cost more than just buying a spare 870 barrel unless you have a friend who will do the work for a case of beer.