It's just a run-of-the-mill Kohler, CH16S I think it was?
Either way, they use the same filter that most of the air-cooled Kohlers used, which is available for any bad boy Kohler-powered mower, if you have a tractor supply company close they have them. 1205001-s IIRC is the kohler part number, may cross over to an automotive filter.
Funny thing. I was "junkyarding" a while back and the particular yard I was at had the cars all marked on the quarter panels what was wrong with them. Trans, Engine, wreck, whatever. I was looking at a bunch of engine failed cars/trucks and a big majority of them had fram filters. I found that odd. Big ol' orange filter sticking out like a sore thumb. I switched brands immediately. But I also understand that sometimes in a pinch you have to do what you can.
Here you go:
http://www.oilfilter-crossreference.com/convert/KOHLER/1205001S