A two letter date code of “WF” indicates August of 1959. 1937, 1985, and 2011 are are also “F” years but are obviously not applicable.
The US Military did continue to buy 513Ts at least into the mid 1960s and while I have seen them in gloss blue, a matte blue stamped “military finish” and the very common military reparkerized finish, they’ve all been marked “US Property” with the USN rifles also marked “U.S.N.
I doubt it’s a USN rifle. If so, it would have been purchased outside the normal procurement process and probably with local funds. Perhaps a NROTC or NJROTC program. If it had CMP paperwork that would support the latter theory.
It’s also probably not an intentional scam, at least by the shop. People give local gun shops and their staff way too much credit. No one can be expert in everything. I’ve had LGS owners insist all kinds of things that just are not true and resulted in the, often unintentionally over representing a gun.
For example a lot of gun shop owners and staff will tell you that a checkered Winchester 9422 is an “XTR” and want XTR . In fact the first year (1978) XTRs were not checkered, so you’ll find uncheckered XTRs, and after the end of the “XTR” grade in 1989, *all* 9422s had checkered stocks. The defining traits of a 9422 are highly polished flats on the hammer and lever, “XTR” stamped on the barrel, and of course a SN falling in the 1978-1989 date range.
If you trust what a shop tells you and don’t verify it with your own research you are well on your way to be disappointed.
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That said I don’t think a U.S. property mark adds much value to a 513T and I would not pay a significant premium for a mI,Italy 513T. They were not exactly rare. However condition is everything and while 513Ts are increasing in value, $650 sounds like a lot for the condition you describe.