I won't even bother responding to the first poster who thinks I don't understand the difference between a composer and orchestrator. I may be abrasive and obnoxious, but I'm a 20+ year veteran of this industry and know what I speak of.
With respect to your post, Gypsy, you're correct. Alex does much more than notate or arrange or orchestrate. I would approximate he writes about 99.1% of the underscoring (Lin primarily writes melodies, lyrics, and comes up with a few musical motifs), which makes him a ghostwriter. It's one of the worst kept secrets in show business although you'll never hear any official comment on it because, well, then he wouldn't be a ghostwriter anymore.