Saying the kid is into Japanese books are very vague in terms of interest, if you consider that anime/manga are huge now. I'm assume mom is somewhat clueless and her kid is at least adept in using the Internet.Snipped
Her kid being 15, zoomer. So high chance of the kid already knows popular anime for "normies" like Hero Academia, Demon Slayer, One Punch Man and maybe Jujutsu Kaisen.
Older big shounen manga (One Piece, H x H and FmA) are okayish. But the autistic long running series is very daunting to get into, not to mention the art style back then is dated comparing to newer ones. HxH suffers with hiatus, which is not great. Especially if you'd like the kid to get into many series, I don't recommend the ones are still ongoing for ages. Anime maybe, manga is kinda a no from me. Only FmA is solid choice imo.
Unpopular opinion, I don't like Rurouni Kenshin. For some reasons, I feel the fictional fighting style, character strength and the theme along with settings are so conflicted to me, that I just outright dislike it. If it has used a different setting, a much less authentic setting then it maybe more acceptable to me.
Recommending more serious seinen stuffs are to be cautious, Blame, Black Lagoon, Vinland Saga, Vagabond, No Guns Life and Psycho Pass. Mostly more mature theme and maybe some slow pacing aren't that "interesting" for the kid age range. Psycho Pass aren't available in manga that much last time I check. Although I don't think Black Lagoon and Psycho Pass are that hard to get into for the kid age, as in good recommendation here.
Depends on how the mom is okay with her kid watching/reading gore, nudity stuffs and ecchi fanservice. At least what level is okay to the mom. Which are from some previous seinen stuffs, Akira, Tokyo Ghoul, Chainsaw Man, Spice & Wolf and Ranma 1/2. Probably Akira is good here, since it has the movie format.
As vern mentioned before, it's probably better to ask for more infos about her kid interest/preference or what they know.
Also, from me, recommending stuffs for parents and kids, it's good idea to consider parental guidance. I feel like people kinda neglecting this a bit much. Especially if parents kinda clueless about a medium, they can have misunderstand/wrong feeling about their kids.