It depends a little bit on what distance you're making the jump from. Going to 60' from Little League majors distance of 46' is a big jump whereas making the jump from a travel ball distance of 50' or a junior high distance of 54' isn't as bad.
Regardless, I think it's best to make the transition slowly to avoid getting the pitcher into a deficit - epecially if the pitcher is starting high school because the high school season does not leave time to recover from a deficit. Start with a couple short (about 25 pitches) bullpens per week. Increase the number of pitches each week. Play catch on non-bullpen days and even do some long toss. But keep it limited at first and slowly increase the number of throws over time. Plan to spend 6-8 weeks making the transition.