It is quite clear that in perfectly elastic head on collision, when two equal masses collide with each other, then they exchange their speeds.
In the present case, bob A is moving with certain speed and bob B is at rest. So after collision, bob A comes to rest and the bob B starts moving with the speed of the bob A. The bob A transfers whole of its momentum to bob B and so, bob A, will not rise at all after the collision. 2
Note : The Bob shall not rise because when two bodies of same mass undergo an elastic collision, there velocities are interchanged and Ball A rests and Ball B moves.