Why can’t mosquitoes spread HIV & AIDS?

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Experts have expressly said that mosquitoes can’t spread the HIV & AIDS virus from one person to the other. This reasoning has remained uncertain to me. When I see mosquitoes, I start imagining how come they don’t spread the virus. Medical experts say the virus cannot survive on the beak of the insect, and that’s the reason why. I concur with the medical experts because if it were not so; all of us could be infected by the same mosquitoes. I thank God for the researchers. However, think of two people sleeping on one bed, one is positive and the other is negative. Imagine if one mosquito bites each of them simultaneously starting with the positive viral loaded person to the one without. Assume this happens within a span of a second, could it be risky to the safe person? I trust what experts in the medical field have said, but in practice, I can see some danger here. If surely mosquito beak does not transmit the HIV & AIDS virus, then I would suggest that the same experts should research on the nature of mosquito beaks (what makes them not spread the virus)and if possible come up with ways of getting the cure for the virus from the same beaks. I am just asking as a layman in the medical research field. What is your take on this?