I recommend reading the information available here: https://www.archives.gov/veterans/military-service-records. Regrettably, the National Personnel Records Center is currently closed due to the pandemic. When it reopens, you will be able to send an inquiry there. You can obtain a veteran's Official Military Personnel File, or OMPF. Since your father-in-law was discharged more than 62 years ago, the records are categorized as archival and a fee is charged.
I hope this information is helpful. If you have any further questions, feel free to ask.
Dear Ms. Holland,
Thank you for posting your request on History Hub!
We suggest that you request a copy of his Official Military Personnel File (OMPF). OMPFs and medical records of enlisted men of the U.S. Navy who were separated from the service after 1885 and prior to 1958 are located at NARA's National Personnel Records Center (NPRC), (Military Personnel Records), 1 Archives Drive, St. Louis, MO 63138-1002. To request these records, please mail a completed GSA Standard Form 180 to NPRC. Veterans and their next of kin also may use eVetRecs to request records. See eVetRecs Help for instructions. For more information see Official Military Personnel Files (OMPF), Archival Records Requests.
Due to the coronavirus public health emergency, the NPRC closed again as of November 7, 2020 until further notice. NPRC will respond only to requests involving burials, medical emergencies, and homeless veterans. If your request is urgent, please see Emergency Requests and Deadlines or emergency requests may be faxed to (314) 801-0764. Please check archives.gov/veterans for updates to the NPRC operating hours and status. We apologize for any inconvenience.
We hope this is helpful.