The answer I was given was that it is theoretically possible but highly unlikely, as the mosquito would have to ingest the blood of an HIV+ person and then almost immediately insert its proboscis into another person so that they can become cross infected.
The HIV virus only lives for an extremely short period outside the human body and it is not normal procedure for a mosquito, having inflated itself with blood from one person, to go directly to another.
Edit :
HIV from Mosquitoes - Bug and HIV - Mosquito HIV Risk
.... answer ... no!