Mr. Gelber noted that the national library in Jerusalem contained papers of such major Jewish personalities as Einstein and Martin Buber, and so it would be a natural home for Kafka’s as well.

This is far from a universal view, however. To many, Kafka’s novels and stories of existential despair written in German seem more consciously worldly than linked to any nationalist movement. The claims on Kafka by German or other archives seem to them just as strong.

A new book, which coincides with the 125th anniversary of Kafka’s birth, “The Tremendous World I Have Inside My Head: Franz Kafka: A Biographical Essay” by Louis Begley, argues that Kafka was deeply ambivalent about his Jewish identity, indeed about any collective identity.

“I admire Zionism and am nauseated by it,” Mr. Begley quotes from Kafka. Also: “What have I in common with Jews? I have hardly anything in common with myself, and should stand very quietly in a corner, content that I can breathe.”

In response, there is a whole scholarly arsenal wielded by Mr. Gelber and others showing that Kafka learned Hebrew (his exercise books with vocabulary still exist), took the Zionist project seriously and had even hoped to move here. In 1949, for example, Kafka’s last lover, Dora Diamant, in whose arms he is said to have died a quarter century earlier, wrote to Mr. Brod saying Kafka’s lifelong dream was “to make aliya and come to Israel,” using the Hebrew word for immigration to Israel.

Some here note that papers as precious as those belonging to Kafka and Mr. Brod may not be legally taken out of Israel without the national archives having a chance to register and make copies of them. But Ofer Aderet, a reporter for the newspaper Haaretz who has written extensively on the Kafka papers, notes that many suspect that Esther Hoffe successfully evaded the law.

Now the question is how her daughters will act. Hava Hoffe took care of her mother in the apartment for years and seems to be in charge of the issue. She is not well loved by most of her neighbors because of the scores of cats she adopted over the decades, giving them free rein to the apartment and front yard.