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Dear Ms. Yerofeyeva,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the Population Schedules for the 1940 Census in the Records of the Bureau of the Census (Record Group 29) that may include him if he arrived before April 1940. These records are digitized and are available online using the Catalog. They are arranged by state, thereunder by county, and thereunder by enumeration district.
The 1940 census is also available on Ancestry. In response to the COVID-19 pandemic, the National Archives has partnered with Ancestry to make the vast majority of their NARA-digitized holdings freely available to the public. Anyone with Internet access may create an account, access NARA records, and use other Ancestry resources, such as their educational offerings and family tree-maker application. For more information see Ancestry’s announcement -- “Free At-Home Education Resources From Ancestry® and Access to Nearly 500M National Archives Records”.
To search for his arrival to the U.S., please check the NARA web page regarding 1800-1957 immigration records.
Since he arrived in the U.S. during the 1940s, he may have completed an Alien File or A-File. Created by the Immigration and Naturalization Service (INS) beginning in April 1944, A-Files contain all records of any active case of an alien not yet naturalized as they passed through the United States immigration and inspection process. An A-File might also be created without any action taken by the alien; for example, if the INS initiated a law enforcement action against or involving the alien. A rich source of biographical information, A-Files may include visas, photographs, affidavits, and correspondence leading up to an alien's naturalization, permanent residency, death, or deportation.
A-Files for the entire United States and its territories are being centralized at the National Archives at Kansas City (RM-KC). Because of strong interest and advocacy for the A-Files by local research communities and their congressional representatives, the National Archives at San Francisco (RW-SB) will maintain some of the available A-Files from the INS district offices located in San Francisco, Honolulu, Reno, and Guam. Researchers seeking individuals who may have lived in these areas should check both the National Archives at San Francisco and Kansas City records for A-Files. Some A-Files still are in the custody of the USCIS and may be requested through the USCIS Genealogy Program.
We hope this is helpful. Best of luck with your research!