A letter of congratulations may be written as such:
1. for achieving a personal goal:
Dear (name),
Congratulations! All of your hard work has finally paid off! I knew that if anyone could (type of accomplishment) it would be you. It takes a great deal of talent, effort, and determination to achieve such a challenging goal and, it is very inspiring to me to see you realize it.
If you have some free time, I would love to celebrate this wonderful achievement with you. Once again, congratulations - I am very proud of you.
2. for a promotion:
Dear (name),
Well, I knew it was only a matter of time before your superiors would reward all of your hard work and brilliance with a promotion. Congratulations on your new position. Your skills and smarts will surely serve you well as the new (name of position).
Best wishes for continual success. I can not wait to see how impressed everyone will be when you start to make a real difference in the (name of department).
I am extremely confidant that your future holds many more promotions of such prestige.