According to the BATFE NFA Handbook
ATF E-Publication 5320.8
Revised: April 2009
in section 6.2.1 Description of firearm.
"...All NFA firearms must be identified by a serial number and other specified markings. If an existing firearm is being used in the making of the NFA weapon, and that firearm is serialized, the existing serial number should be used (unless it duplicates a serial number already used by the maker on Form 1) and entered in Block 4(g)."
"...The serial number must be engraved or stamped on the receiver of the firearm and the caliber, model, and identification of the maker must be engraved on the barrel or frame or receiver of the weapon. The marking and identification requirements for a maker are the same as for a manufacturer. Refer to section 7.4 for a detailed discussion of the requirements."
7.4.1 Serial numbers.
"Each manufacturer of a firearm must legibly identify it by engraving, stamping (impressing), or otherwise conspicuously placing on the firearm’s frame or receiver an individual serial number not duplicating any serial number placed by the manufacturer on any other firearm."