I am not for sure if it will work or not. I know you can send them back to HMF and they will reprogram for you. All you have to pay is shipping both ways. I know because they have reprogramed 2 units for me.
Yes they will work on both, dobeck makes them as well as muzzy and many others the one I had for my 1000 stated in the box it would fit '07 800,650,500- programming is not as big of an issue is the plugs, that's the big diff
The main difference requiring different program is when putting on a bike with different injector sizes. But by the EJK website - its all the same box anyway for all years and sizes. Not sure if HMF does anything different.
You should be fine using 07 650 one on the 07 800. (as fine as it could be anyway)