More recently, as the cost of Ms. Sheard’s care increased, she and her family decided to sell the letters to the Morgan, which collects and displays Salinger correspondence. (The museum declined to say how much it paid for the letters.)

Liza Sheard, a niece of Ms. Sheard’s, said in a telephone interview that the letters held a strong sentimental value, particularly because her aunt never became a published writer and lived most of her life as a housewife in a modest apartment.

“It’s fantasy-like, because this was not her life at all,” Liza Sheard said. “It’s a young woman writing to a superstar and talking to him as if they were peers.”

In their earliest, playful exchanges, Salinger says he is rereading “Anna Karenina,” which he says is not as good as “War and Peace” but “a far craftier job.” (Of Tolstoy, he writes cheekily, “I think he’ll go places.”)

In addition to recommending his own stories, he suggests that Ms. Sheard read “The Great Gatsby” and “The Last Tycoon,” by F. Scott Fitzgerald. She replies that both Fitzgerald and Ernest Hemingway “annoy me in the same way — one feels oneself tricked into feeling sympathy for entirely undeserving and rather tiresome people.”

But at the start of 1942, Salinger’s correspondence takes a sardonic turn, and he asks Ms. Sheard not to bring up his as-yet-unpublished Holden Caulfield story. “God and Harold Ross alone know what that bunch of pixies on the staff are doing with my poor script,” he writes, referring to the founding editor of The New Yorker.