The number on the butt is the legal serial number of the gun, period. No need to second guess. The number in the yoke cut is supposed to be the same and was reportedly added for the convenience of police agencies to be able to verify the SN of guns that had target stocks without removing the stocks . . .
If you're saying that the only legal place for the serial number to reside is on the butt . . . I respectfully disagree.
Title 27 Code of Federal Regulations (CFR) 478.92(a)(1) and 479.102(a) further require the licensed manufacturer, licensed importer, or maker of a firearm to legibly identify each firearm manufactured, imported, or made by engraving, casting, stamping (impressing), or otherwise conspicuously placing the individual serial number on the frame or receiver, and certain additional information - the model (if designated), caliber/gauge, manufacturer/importer's name, and place of origin - on the frame, receiver, or barrel.
As I read the above BATF Regulation, the serial number must appear on the frame. The butt is certainly part of the frame and is customarily where S&W places the serial number. The yoke cutout is part of the frame . . . as is the front of the grip strap where Regulation Police models have their "legal" serial number placed. And the factory has been known to re-stamp the legal serial number on the left side of the grip frame when the hole for a lanyard ring was drilled through the serial number on the butt.
If I had the OP's example I would want both serial numbers on the frame to be the same . . . and not with one belonging to a different gun.
Russ