I have just replaced an 03 FJR with an 06, and of course found that my old Givi rack didn't fit the new bike. So what I did was take the box base plate off the old rack and bolt it to the carrier on the new bike.
I did this by removing the three bolts that presently pass through the top of the carrier, and replacing them with much longer bolts. I bought some aluminium tubing from the harware store, and made some spacers, so that the new bolts pass through the base plate (I drilled suitable holes), through the spacers, and into the origional threaded holes.
The top box base plate is therefore mounted on stand-offs above the existing carrier. There is just enough room between the bottom of the top box and the base plate to accept the heads of the new bolts.
I have so far done 900 Km with this arrangement, and no problems so far. Cost less than $20.
I have a Givi E52 Maxia top case from a previous bike & e-mailed givi-usa about a bracket/adapter plate for the 2006 FJR. They replied that the part # SR357 will be available by the end of May with a cost of $142 dollars. You will have to remove the current carrier/grab rails.