Can a good 2003 OEM cat be used to replace a bad OEM cat on a 2005 or 2006 STR? If not, why?

 

Have you tried to see if the part numbers are the same?

 

They all old at this point and I would install an new aftermarket one instead.

You could very easily install the used one and find out it's not working enough to pass inspection or it sets check engine lights or that it fails or clogs in a short time.

Just not worth the risk as a new catalytic converter (NOT from Jaguar!) is not that expensive and you will need to pay for installation for either one you get.
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The part Numbers are different. Does any one know if the 06 Superseded the 03 part number. and if the 06 is a compatible replacement for the 03?

06 = 6R83 5E212 DA
03 = 2R83 5E214 JC