I have a service manual. The seller took the picture, not me. I can ID air filter, clutch, and some covers. The part attached to the large gear in the cover at bottom right appears to be a sprag clutch, I'm not sure what the damper that's problematic on the 2003 looks like, but the parts fiche appears significantly different between the two so I'm not sure how my service manual would help.
Is the damper attached to the smaller round cover at bottom left?
Yes, that is the damper on the lower left... if you want to do the upgrade on your 2003 without buying any other parts
you should get the damper, the cover it is sitting in, and the stator cover to the right. You don't really need any of the
other parts for that upgrade but if they are cheap grab them anyway for spares.
You CAN use your stator cover, but you need to buy a bushing from Yamaha to make it work.