Yes, it's possible to hoist the child up.
Let's first determine the maximum amount of pull that the woman can exert. That will be the simple product of her weight and the coefficient of static friction with her shoes and the ground. So
0.8 * 190 = 152.
So far, so good, since 152 is greater than the boy's 80 lbs. But the cable rubs at the cliff edge and that means that the lady has to pull harder. Let's see how much harder.
There will be 80 lbs of tension on the cable, pressing against the cliff edge. So let's multiply by the coefficient of friction to get how much that is
0.2 * 80 = 16
So friction will take 16 lbs of effort to overcome. So the lady needs to pull with 80 + 16 = 96 lbs of force to move the boy. And since we've determined earlier that she can pull with up to 152 lbs of force, she can easily hoist the child up.
