Stimulant medication reduced sleep latency (the amount of time between going to bed and falling asleep), and reduced the amount of times people awoke in the middle of the night.  Study participants also reported improvement with their sleep pattern.  They felt they were more refreshed upon awakening.  Study subjects took methylphenidate twice a day.

It could be that taking medication for ADHD improves efficiency and overall functioning, leading to an improved mood and reduction in frustration and stress.  Or the medication may allow the brain to rest, thus helping it fall asleep faster.  Or it could be a combination of the two. Or an entirely different reason.  

The study was not funded by a pharmaceutical company.