Alexander Solzhenitsyn met Kobozev in August 1960 through , former post-graduate student of Kobozev and the first wife of A. Solzhenitsyn. Reshetovskaya brought Solzhenitsyns manuscript (later entitled "One day of Ivan Denisovich") to her former professor. Kobozev had developed much interest in Solzhenitsyns ideas and asked his wife for an introduction. The family of Kobozevs executed brother kept all Solzhenitsyns primary manuscripts between 1962 and 1969.
Due to Kobozev's severe health conditions, they met only at his apartment almost every evening until his death. Solzhenitsyn confessed in his account that Kobozev had had enormous impact on his views and "was the smartest man he had ever met". Solzhenitsyn made multiple attempts to help the professor with his health, including finding doctors and foreign medicines, but nothing ever helped.
In Solzhenitsyns English-language memoir Invisible Allies', a profile of Kobozev and their friendship comprises Chapter 2.