Who said there is such a letter ?

I never heard of it

Mars, there are several threads on the topic. Once you pass the exam, you either get a letter from NASBA (I think?) or your state board if your state is not a NASBA state.

Jcamp, my state isn't a NASBA state and I got my letter 5 days after I received my last passing score. I've heard that NASBA state candidates have to wait several weeks before receiving their letters, as they all get sent out at once. I could be wrong about that, though.

According to NASBA...

"The congratulatory letters will be mailed to candidates by the following dates:
January/February testing window: May 15
April/May testing window: August 15
July/August testing window: November 15
October/November testing window: February 15"

For me seems to be a long wait for the letter, but maybe somebody else could confirm if they send the letter before that dates.