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I believe what you'd want is:
Hi dear friend,
I know we haven't talked much or at all since you moved to focus on your studies. I really miss you and hope you can return this letter. Things just haven't been without you in our friend group. I do hope you're getting good grades and you'll get that degree! I also hope you can come back home soon. Things have been crazy over here. (You can add something you've been doing or just something you can think of. Pets, grades, new friends, maybe your gaming.) But back to you, you were always a good friend and student. I'm sure you'll have no trouble passing. We all believe in you!
From, (Your name)