I started with the Jeweler and found it in Burlingame, CA. It opened in 1944. While re-handling the outer box, I realized there was a period photo labeled with a family name wedged in the box top, so I decided to see where I could take it. Watch came from AZ, so I started there. Much to my surprise, I got 3 obituary hits for the same man W.M.Moeller. He grew up and lived in Iowa and served in the Navy on a ship in the Pacific as a radio operator. Moved to Arizona in 1992, where he died in 2020; one week short of his 100th birthday. Watch was mailed to me by a seller about 100 miles from his last residence.
Here is the photo from the box along with a photo from one of his obituaries.
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The biggest puzzle at this point was the jeweler. The single internet hit was in California and the store sign and logo match the paperwork signature "Kerns". The dates were good but why was a farmboy from Iowa in CA? The answer was found when I researched the ship he served on. The attack cargo ship USS Arcturus (AKA-1) served in both the Atlantic and the Pacific. Moeller's obit said he served from March 1942 - Nov 1945. On 15 April, 1944 Arcturus received orders to Saipan where she was routed on to Pearl Harbor and San Francisco, arriving at the latter port on 18 May. After loading cargo and supplies, Arcturus returned to the western Pacific to resupply the troops advancing on Okinawa.
There was my answer. San Francisco Naval yard is about 20 miles from the jewelry store. That placed Mr. Moeller within a few miles of watch origin in 1944, the year the store opened and a shore pass away from his ship..
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Commodore - U.S. Navy history. Historically, the title was given to a commander who was the captain of a ship, but was in command of a grouped element of ships, often called a squadron.