Ah, ha! Number on yoke visible through charge hole is 336664. Hmm, so does that mean serial is C336664? That would make it, what, 1955? So, what should I tell the owner to do?
I think you have a 1948-1955 frame on which a barrel, cylinder and hammer from a decade or more later have been installed. Trigger too, probably. The original serial number was polished off and the created serial number that you see was applied to the butt and (without the alphabetic characters) the flat underside of the barrel.
I don't know if you can tell without removing the cylinder from the gun, but is the gas ring part of the cylinder or part of the yoke?
Does the ejector rod screw in with a right-hand thread or left? Left means the cylinder assembly is post -1961.
I wonder if the serial number we see now was dictated by ATF as part of a gunsmith repair. I have no idea how such things work. I know that guns can be reserialed, but not if they could have had a US prefix.
Not a collectible, but potentially a decent shooter and possibly legal. (Not that I would bet on its legality if the serial number was modified in an unapproved manner.)
I suspect the yoke is original and that the number reflects the original identity of the frame: C336664. In that case, the gas ring would still be on the cylinder, but the unnumbered cylinder points to either a factory-provided replacement part or original installation on a later revolver from which it was removed to be installed on this frame. About 1957-58 the factory began the practice of NOT numbering parts with the serial number of the frame.
That looks like a 10-5 barrel to me. What do the roll markings on the side of the barrel say? I would expect the caliber designation to read .38 S&W SPECIAL CTG, but in the whole-gun photo it doesn't look like the stamp is long enough to contain all those characters. On the other side it should just read SMITH & WESSON.