Short answers, pulled from the story.
Martin Heidegger wrote the letter in December 1946. Jean Beaufret sent questions on the 10th of November 1946. The exchange began with this specific date and ended with Heidegger's response months later.
The correspondence concerned French existentialism and Sartre's work titled Existentialism is a Humanism. Heidegger addressed Sartre's address to ground freedom ontologically using modes of being. This moment marked the start of a public philosophical debate known as the Letter on Humanism.
Sartre claimed that existence precedes essence while Plato had said that essentia precedes existentia since ancient times. Heidegger argued that Sartre took existentia and essentia according to their metaphysical meaning and reversed this statement. Heidegger insisted that reversing a metaphysical statement remains a metaphysical statement and leaves thinkers in oblivion regarding the true nature of Being.
Klostermann published the final version in Frankfurt am Main in 1949. The initial draft appeared in December 1946 as a response to Beaufret. William J. Richardson documented this history in Martin Heidegger: From Phenomenology to Thought which appeared in 1967 on page 351.