September 26th, 2016, 12:32 PM
Joined: May 2005
From: Sacramento California
I Ride: "2000" FE600, 1996 FC600, 1984 Husky WR400, 2015 Beta Xtrainer
For a '96 FC600, not only is there no oil filter, but there is no oil pump either. The only filtration is from the "screen" that you're referring to as "washable". That screen is in place to discourage larger parts - nuts, bolts, boulders, cats - from entering the transmission.
Change your oil very often on that one. I have 2 FC600 engines in the vintage of '96 and a '95 FE501. They're wonderfully simple.