Kheifetz first contact with J. Robert Oppenheimer came at a party to raise money for Spanish Civil War refugees hosted by Kheifetz's mistress, Louise Bransten on December 6, 1941, the day before Pearl Harbor.  Kheifetz managed to meet Oppenheimer alone for lunch later in December 1941 where Oppenheimer told Kheifetz about the Einstein-Szilard letter to President Franklin Roosevelt and provided details on the current status of the US atomic research program.  Kheifetz advised Moscow by cable from Washington that the outstanding physicists in the Allied world including Nobel Prize winners and giants like Albert Einstein, were involved in a secret project. This changed Moscow's attitude toward about the atomic project.
California on the Crimea
In 1943 a world-famous actor of the Moscow Yiddish State Art Theater, Solomon Mikhoels, together with well-known poet Itzik Feffer, toured the United States on behalf of the Jewish Antifascist Committee. Before their departure, KGB Chief Lavrenti Beria instructed Mikhoels and Feffer to emphasize the great contribution of Jews to science and culture in the Soviet Union. Their assignment was to raise money and convince American public opinion that Soviet anti-Semitism had been crushed as a result of Stalin's policies. Kheifetz made sure that the message they brought was conveyed to Manhattan Project Director J. Robert Oppenheimer.
In 1944 and the first half of 1945, Stalin's strategic motivation was to use the Jewish issue as a bargaining chip to bring in international investment to rebuild the war-torn Soviet Union and to influence the postwar realignment of power in the Middle East. Stalin planned to use Jewish aspirations for a homeland to attract Western credits.
Intentions to form a Jewish republic actually existed, based on a letter addressed to Stalin from the Jewish Antifascist Committee. Part of the letter, published for the first time in 1993, stated:
The creation of a Jewish Soviet republic will once and forever, in a Bolshevik manner, within the spirit of Leninist-Stalinist national policy, settle the problem of the state legal position of the Jewish people and further development of their multicentury culture. This is a problem that no one has been capable of settling in the course of many centuries. It can be solved only in our great socialist country. 
The letter, whose existence is officially admitted in the journals of the Communist party,  is still not declassified. Kheifetz said the letter was a proposal with details for a plan to make the Crimean Socialist Republic a homeland for Jewish people from all over the world.
Coordination and execution of Stalin's plans to lure foreign investors was entrusted to Kheifetz. The Soviet plan was for him to lay the groundwork for American investment in the metal and coal mining industries in the Soviet Union. It was rumored that Mikhoels might be offered the post of chairman of the Supreme Soviet in the proposed new republic. Apart from Molotov, Lozovsky, and other high-ranking officials in the Ministry of Foreign Affairs, Mikhoels was the only one aware of Stalin's plans to establish another Soviet republic. Stalin hoped to receive $10 billion in credits from the U.S. for the restoration of the Soviet economy after the war.
The plan to lure American capital was associated with the idea of a Jewish state in the Crimea was called California in the Crimea. Kheifetz widely discussed the plan in America.
Kheifetz and Oppenheimer discussed Stalin's plans to set up a Jewish Soviet Socialist Republic homeland in the Crimea after the war was over. Kheifetz said that Oppenheimer was deeply moved by the information that a secure place for Jews in the Soviet Union was guaranteed. 
With the help of Elizabeth Zarubina, the wife of North American Rezident Vasili Zarubin, Kheifetz and Zarubina persuaded Oppenheimer to share information with "antifascists of German origin," which provided a rationale for taking Klaus Fuchs to Los Alamos. Oppenheimer agreed to hire, and promote these people, provided he received confirmation of their opposition to Nazism before they came to the project. Under Oppenheimer's initiative, Fuchs was given access to material that he had no right to look at. 
By 1943 it was decided in Moscow that all contacts with Oppenheimer would be through unregistered illegal agents only. Lev Vasilevsky, the Rezident in Mexico City was put in charge of running the illegal network after September 1943. Kheifetz and Semyon Semenov were instructed to turn over all their contacts around Oppenheimer in California. So secretive was the operation that under Beria's direct orders Kheifetz and Semyenov were instructed not to tell anyone in the Soviet Foreign Intelligence service about the transfer of contacts to the Mexico City Rezidentura. 
A memo from Vselovod Merkulov to Lavrenti Beria dated October 2, 1944 read:
In the period 1941-1943 important data on the start of research and work in the USA on this problem [uranium] was received from our foreign agent network using the contacts of Comrades Zarubin and Kheifetz in thieir execution of important tasks in line with the Executive Committee of the Comintern. In 1942 one of the leaders of scientific work on uranium in the USA professor Oppenheimer unlisted member of the apparrat of Comrade Browder informed us about the beginning of work. 
Kheifetz described Oppenheimer as a man who thought of problems on a global scale.
- The Venona Story, Robert L. Benson, Center for Cryptological History, National Security Agency.
- Pavel Sudoplatov, Anatoli Sudoplatov, Jerrold L. Schecter, Leona P. Schecter, Special Tasks: The Memoirs of an Unwanted Witness -- A Soviet Spymaster, Little Brown, Boston (1994), pg. 175.
- Jerrold Schecter and Leona Schecter, Sacred Secrets: How Soviet Intelligence Operations Changed American History, Brassey's Inc., Washington, DC, 2002, pgs. 47-49.
- Literaturnaya Gazeta, July 7, 1933.
- Izvestia CC CPSU, no. 12, 1989, p. 37. The letter was not shown with the archival material of the Jewish Antifascist Committee that was displayed in Washington, D.C., during President Yeltsin's visit in 1992.
- Special Tasks, pg. 50.
- Special Tasks, pp. 190, 193.
- Special Tasks, pg. 3.
- Allen Weinstein and Alexander Vassiliev, The Haunted Wood: Soviet Espionage in America—the Stalin Era, Random House, 1999. ISBN 0788164228
- Special Tasks, pgs. 187.
- Merkulov to Beria, 2 October 1944.
- Was Oppenheimer a Soviet Spy? A Roundtable Discussion with Jerrold and Leona Schecter, Gregg Herken and Hayden Peake. The Cold War International History Project. The Woodrow Wilson International Center for Scholars.