In July of 1939, he wrote to her that he was happy that
you've finally read Heidegger, it's worth your while and we'll talk about it.
Later the same year, he records his impressions of Paris in its last pre-war late summer. Even Sartre's mundane ruminations on travel are affected by his reading of Heidegger:
Paris was very strange. Everything was closed, restaurants, theaters, stores, because it's August, and the neighborhoods had lost their individual character. There was only one totality left, Paris itself. A totality which, for me, was already a thing of the past and, as Heidegger says, retained and upheld by nothingness.
His reference to Paris as 'a thing of the past' may be because he's getting ready to leave, or because his sense that soon war will change it. In either case, once he has left (to resume his military service), he writes to Simone de Beauvoir about his fellow officers, even describing one's personality in Heideggerian categories, in a letter dated 6 September 1939. A few weeks later, he explains how he departs from Heidegger in his own thinking:
All of man's acts, being accomplished by means of the body, are registered finitely on a double infinity - of immensity and minuteness. And from that fact, all consideration of objects as implements brings human reality to the consciousness of its own disregard. For what Heidegger did not see is that the infiniteness of the world surpasses its implementicity in every direction.
He continues:
If the vast distances to the stars produce a stupor akin to Pascal's terror, that is because it comes from the transcendent infinite of the transcendental consciousness - and, at the same time, the perception of the stars necessarily includes an attempt at their implementation which conflicts with their “out-of-reach” quality. Heidegger didn't see that his world for man - which is indeed immediately and pre-ontologically an implement - is coincidental with man and not wtih the transcendental consciousness, and that it is completely surpassed and disarmed by the world for consciousness, which isn't capable of receiving implementicity, across which implementicity slips without being able to grab hold.
In October of 1939, he writes that
I'm mulling over a central idea that will finally allow me to eliminate the unconscious, to reconcile Heidegger and Husserl.
Later, he reports that
I attempted a reconciliation of Heidegger and Husserl. It didn't pan out, but I stuck to it doggedly, and I feel quite woozy after six hours' effort. The whole thing must be done over. There is still this entirely circular idea and I don't know where to pick it up, so I grab at it, and it slips through my fingers like a ball of grease. You'll see, it makes for odd little notebooks.
In November, he complains in a letter that one of his fellow officers didn't understand a Heidegger book which Sartre had lent to him; presumably most of Sartre's fellow officers would have been in that situation, although Sartre seems to think that after weeks of trying, they've begun to understand a bit of Heidegger. These were the long weeks after war had been declared in the autumn of 1939, but before actual fighting began in early 1940. Such officers had lots of time for conversation, but with an ominous or foreboding sense about the future. Sartre notes that
Human reality is of a particular existential type, as constituted by its existence in the form of value to be realized through its freedom. This is what Heidegger expresses when he says that man is a being of distances.
Even as Heidegger's influence on Sartre makes itself ever more felt, Sartre discovers Kierkegaard's influence on Heidegger. He writes in another letter to Simone de Beauvoir about Kierkegaard's book
The Concept of Dread, in which there are countless things within theologic terms that are obviously a bit forbidding. His influence on Heidegger is undeniable.
In another letter, dated December 1939, Sartre continues, telling her that he's continuing to study
The Concept of Dread, which I'll send or bring back to you, and which you'll read with the greatest of interest, if only to understand Kierkegaard's influence on Heidegger and on Kafka (you know that Kafka feathered his nest through that book).
It becomes clear, through these letters, that 1939 was a pivotal year for Sartre's intellectual development, and that Heidegger influenced him greatly during this time.