Who sends the "Letter from Friend"?
Solution 1:
He is a plot device. It is never explained who "A Friend" might be.
As for how he knows you're Dragonborn, well, it's not every day that you see somebody FUS RO DAH'ing left and right and absorbing dragon souls...
Solution 2:
The game never tells you who he is, but probably it's not someone with a name since you can meet this someone and you'll still receive letters, maybe It's a NPC like "Stormcloak Soldier" or even the courier.
I always thought it was the courier, and It's not hard for people to discover who is the dragonborn.