It's possible that the hardware architecture of the Foxhunter is incompatible with the operating system required for utilising the AIM-120, thus precluding the possibility of software upgrades.
If that is the case (a bit like trying to run a Mac program on an IBM) then the only option is to change either the electronics in the missile, which is probably not feasible, or the radar in the aircraft, which is possibly not economic.
BEagle's idea makes perfect sense.....but if the powers that be were looking for another excuse to bin the SHar, wouldn't it be convenient if they had to refit the F3 with Blue Vixen, and that the only economically viable means of doing so was by utilising existing units?