It was a Remington 1903, Remingtons with serial number ranges from 3000001 to about 3348085 were standard 03s produced in 1942. At 3348086 production changes to 03A3s.
I'm actually pretty well versed on 1903 Springfields since I've been playing with them since my first in 1968
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FYI: There are two variations of Remington 1903. The first is the standard 1903. The second is known as 1903(m) or (modified). The 1903(m) transitioned into the use of stampings prior to the 03A3. Most all the Remington 1903 and 1903(m) went to England for Lend-Lease. The one above was from Greece, both were actually. I bought them when CMP first offered them.
Stocks: The original Type S, the pistol grip Type C and the scant grip (see below) are all "correct" on any 1903 rifle that was in U.S. inventory. How they rolled off the assembly line when they were first made is one thing, but after having been in service and through overhauls they could have any of the stock types and still be "correct". And, as was mentioned, a 1903 or 03A3 could pick up a new stock from a civilian owner since these rifles have been in civilian hands since the 1950s or 1960s. I bought a nice Type C stock once for $25 and put it in a $50 03A3 and it made a real nice rifle. Loosing sleep over what's correct and not correct will cause premature aging
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Best book on the subject: Brophy's "The 1903 Springfield". Hatcher's Notebook is a must for any 1903 rifle enthusiast. And Bruce Canfield's Infantry Weapons of WW1 and the 2nd book Infantry Weapons of WW2 are not bad reference books.