matching numbers?
 

Is there a definitive book that give specific vin# and what engines came with those from the factory?

No.

The only exception that I know of is the '73 Carrera. The book Carrera RS lists all the chassis #s along with their engines, transmissions, options, color, interior, etc.

as well for 904 and 906

How do you know if the engine and gearbox is original to the vehicle?

As far as I know, Porsche offers a service to verify your engine and VIN number with their files.

There are several books that give the range of VIN engine trans numbers that would be possible in a given year, but not individual matches are available publicly.
You have to pay PCNA about $100 and they will issue the COA containing the numbs and other info for your car.
Certificate of Authenticity - Owner Services - Porsche Service - Dr. Ing. h.c. F. Porsche AG

Thanks for the info, I think I'll spend the hundred bucks on gas instead!

Definitely a more enjoyable choice!

That Cert. of Authenticity is definitely a $100 gamble. If you look into as I did, they will print up "whatever information is available" for your particular car. What the info is, you won't know until the certificate shows up and your bank account goes down $100. This is what the application to get a certificate says.

" We are pleased to offer you a Certificate of
Authenticity for your Porsche. This unique
document includes your vehicle’s original
factory-installed options, exterior and interior
color, engine type and transmission type,
production completion date (Birth Date) and
manufacturer’s suggested retail price
(MSRP), dependent upon availability of
information. Only vehicles produced for sale
in the US or Canada are eligible for North
American Certificate"

Engine type and engine serial number are 2 different things. I looked into getting one to find out what my car cost new. However, that little statement "dependent upon availability of information", stopped me.

Other than doing as suggested by the books with general numbers in them, you could poke around the engine compartment and look for dates on parts and compare that with the build date of the car. Perfect example I know my exhaust is original not becuase it has a Porsche part number, but it's date stamped Jan 82. My car was built in Oct. '82. If you poke around and look at sending units, and even some plastic parts will have a month/year stamp on them.