One of the most prevalent myths about HIV transmission is that mosquitoes or other bloodsucking insects can infect you. There is no scientific evidence to support this claim. To see why mosquitos don't aid in the transmission of HIV, we can look at the insect's biting behavior.
When a mosquito bites someone, it does not inject its own blood or the blood of an animal or person it has bitten into the next person it bites. The mosquito does inject saliva, which acts as a lubricant so that it can feed more effectively. Yellow fever and malaria can be transmitted through the saliva, but HIV does not reproduce in insects, so the virus doesn't survive in the mosquito long enough to be transmitted in the saliva.
Additionally, mosquitoes don't normally travel from one person to another after ingesting blood. The insects need time to digest the blood meal before moving on.