I bought a 624 earlier this year and had similar facts; I did not have the box, so did not know whether the gun was previously checked, and the cylinder had a "F" stamp. I was told that the gun still had to be checked. The F stamp is not a valid check marking. Also S & W has not kept records of the guns actually checked, so they can not match up your serial number to confirm it may previously have been sent for testing.
Fortunately, mine passed and I'm more comfortable knowing that than just shooting lighter loads.
Steve
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