Somewhat the same happened to the wife's 6R. One day it decided it would just crank and crank but not fire, replaced with a new battery and it fired right up, been running great ever since. Not saying this is your issue, just something to consider.
I did a quick look at Partzilla. A 2009 FZ6R part number is different than that of a 2009 FZ6. As far as actual fitment goes, I don't know if that would mean anything or not.
Have the battery load tested. Wife's 6r would crank but would not fire, everything appeared fine otherwise. We replaced the battery and it fired right up, no problems since.