Answer
If the man stops climbing, then the speed of the balloon is zero.
Work Step by Step
Before the man starts climbing up, the initial momentum of the (balloon-climbing man) system is zero.
While the man is climbing up, the momentum of the (balloon-climbing man) system is still zero.
If the man stops climbing, the momentum of the (balloon-climbing man) system is still zero.
Since the man's speed is zero, then the speed of the balloon must also be zero, otherwise the momentum of the (balloon-climbing man) system would not be zero.
If the man stops climbing, then the speed of the balloon is zero.