Per the GCA of 1968 and related legislation, serial numbers are required to conform to certain standards such as size of print and depth of impression. I would proceed on the assumption that the original serial number somehow did not satisfy the legal requirements and so the importer gave the firearm a new serial number that did. That would make the importer's number the "legal" serial number for your bound book.
Then (if it were me) I'd go ahead and enter both numbers in my book anyway just to be on the safe side - I don't see how doing that could lead to any problems.
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