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Dear Mr. Kazlo,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the series titled Logbooks of U.S. Navy Ships and Stations, 1941 - 1983 and Muster Rolls of U.S. Navy Ships, Stations, and Other Naval Activities, 1/1/1939 - 1/1/1949 in the Records of the Bureau of Naval Personnel (Record Group 24). They include logbooks/deck logs and muster rolls of the USS Vixen (PG-53) for 25 February 1941 to 24 May 1946. For access to or copies of these records, please contact the National Archives at College Park - Textual Reference (RDT2) via email at firstname.lastname@example.org.
We hope this information is helpful. Best of luck with your family research!