Over the years, a friend of Mr. Salinger’s, a former lover and even his daughter, with whom he had a difficult relationship, said he continued to write, both exploring new tales and picking up where his published stories had ended. His daughter, Margaret Salinger, wrote in her 2000 memoir, “Dream Catcher,” that her father had shown her his “vault” in his home, where he wrote in privacy and marked manuscripts with colored dots indicating what was to be edited, published or discarded after his death.

Ms. Salinger could not be reached for comment, and her book publicist said she had not worked with Ms. Salinger in years and did not know how to find her.

But all of the claims lacked specificity until “Salinger,” which detailed what Mr. Salinger was said to have written, edited and prepared for publication. The five works came from what Mr. Salinger compiled from 1941 to 2008, according to “Salinger.”

One new book, “The Family Glass,” is said to include five new stories about the Glass family, who also appeared in the 1961 book “Franny and Zooey” and other stories. There would also be a novel set during World War II and based on his first marriage; a novella about his time in the war; and a retooled version of the short story “The Last and Best of the Peter Pans” that would include new stories about the Caulfields, the fictional family in “The Catcher in the Rye,” his signature 1951 book that remains required reading for high school students every year. (Read the original Times review.)

Mr. Salerno, who produced and directed the documentary, said in a recent interview that he stood by the claims. He said the veracity of the assertions in “Salinger” could be questioned only if nothing were published by Jan. 1, 2021.

“How did I ever manage to get any of this stuff without Matthew Salinger?” Mr. Salerno wrote in an email. “It’s very simple, despite his fervent hope to be the only source about his father, Matthew Salinger is ultimately just one source. It’s critical to point out the following: Matthew Salinger has never disputed a single fact contained in either the book or film.”