If I may, I have 2 suggestions that will REALLY help your trumpet player get those parts and develop his upper register, along with endurance and control to boot. WITHOUT a lot of practice time......

1. He needs to develop the "Wedge" breathing technique. Maynard Ferguson learned about it from reading a book called "The Science of Breath". It is a book on Hatha Yoga breathing. It is available free on the internet. Also, he can go to the website "Stars teach music" and for around $10 he can learn it from Roger Ingram, one of Bobby Shew's students and formally lead trumpet with Mr. Ferguson. He explains it in detail. Roger Ingram and Frank Greene both have great books discussing every aspect of upper register control, breathing, embouchure development, etc.
The upper register of a brass instrument is really about 3 things>Airspeed (Fast), Apature position, and a mental "singing" concept of the sound you want BEFORE you play a note. Once you have those ducks in a row, you can just play melodies, concentrating on playing with as much relaxation and ease as possible. Play "Mary had a little Lamb". Rest and then play it a 4th or 5th up. If it still sounds great, continue. If your compression and mental game aren't together, rest.....sing it, then try again. Rest often. Repeat the next day. In a year or so you can expand your Usable range by as much as an octave....no easy feat!!!! This is an alternative to the traditional study methods (Arban, Clark, Schlossberg, Thieke, Irons, etc)

2. Head on over to the Warburton Mouthpiece website. They have a new tool that has really changed the way pro trumpet players as well as students are practicing. They have a product called P.E.T.E., basically it's just a hunk of metal that you insert into your mouth and then the lips grab it and hold it. Far different than the "Pencil" exercise that some use. Results are fantastic. It will not replace a well rounded practice routine. BUT....if you are only playing a couple times a week and don't have the practice time, it will do wonders. Just tell him NOT to overdo it, as I did when I first got it and then couldn't play for 2 days!!!

Ed