After blood passes into the mosquito gut, the parasites quickly turn into male and female forms the gametes and emerge from their hiding place inside the red bloodcells to mate.
In the case of the Mississippi baby, we know she was exposed to HIV, had HIV in her blood, and that at least some cells in her blood were found with sleeping virus though we will likely never know if those cells were from the child or maternal cells that had been transmitted during pregnancy or birth.