JD to Kohler part numbers

[gnfreak]

just wondering if there is a cross reference between John Deere part numbers to Kohler numbers online. 79 spitfire btw. i found the John Deere parts catalog so have all the JD numbers. all the web sites i've visited dont list the K340-2FA engine. local kohler dealer here in town told me that was a bad model number and i must have a japanese motor. i "tried" to tell the guy diffrently but ran out of patience. i've got a few gasket numbers crossed from ebay sales but would like to do this easier. thanks for any help, keith