Stool Angular Momentum Mind Experiment Explanation On pages 639-640 of Newtonian Mechanics by A. P. French it says the following

For example, one person can sit on a pivoted stool [Fig 14-5(b)] and another person can hand him the wheel after it has been set spinning with angular momentum $\mathbf L_W$ as shown (corresponding to clockwise rotation about a vertical axis pointing upward). The person on the stool is not himself rotating, but the system, person + stool, has the total internal angular momentum $\mathbf L_W$. If the wheel is now inverted its rotational angular momentum about its own center of mass is changed to $-\mathbf L_W$. It followed that the system of two masses M (the person) and m (the wheel), must acquire a clock-wise rotation with a total rotational angular momentum of $+2\mathbf L_W$ [Fig 15-5(c)]. If the wheel is in this new orientation is handed to the assistant, who inverts it and handes it back, the total angular momentum is raised to $+3\mathbf L_W$. If the person on the stool again inverts the wheel, the general rotation of M + m is raised to $5\mathbf L_W$.

Shouldn't it be $4\mathbf L_W$? Is this a misprint or am I mistaken? There is the stool axis which has $+2\mathbf L_W$ and the wheel axis which has $+1\mathbf L_W$, and then the wheel is inverted so the stool axis has $+4\mathbf L_W$ and the wheel axis has $-1\mathbf L_W$ and the total remains $+3\mathbf L_W$?
And the handing of the wheel back and forth has no effect on angular momentum because there is no torque involved, but it does affect angular velocity? It speeds up when he first hands the wheel back (assuming he doesn't increase his moment of inertia too much) and then slows down when he gets the wheel back, to the exact same speed if he holds it in the same position?

 A: Initially the system of two masses has a vertical  angular momentum of $\mathbf L_{\rm W}$ and when the wheel is inverted the total vertical angular momentum of the two masses stays at $\mathbf L_{\rm W} = 2L_{\rm W} \,\text {(man)} - L_{\rm W} \,\text {(wheel)}$.
Now remove the wheel so the total vertical of the man is $2L_{\rm W} \,\text {(man)} - 0 \,\text {(wheel)}$.
Re-invert the wheel remote from the man and add it to the man gives a total vertical angular momentum of $2L_{\rm W} \,\text {(man)} +L_{\rm W} \,\text {(wheel)} =3L_{\rm W}$.
Thus each inversion, removal of the wheel, re-inversion of the wheel remote from the man, and addition of the wheel increases the vertical angular momentum of the two masses by $2L_{\rm W}$.
If the person on the stool again inverts the wheel, the general rotation of M + m is raised to $\mathbf 5L_{\rm W}$.
I think that perhaps the author meant the phase . . . . . again inverts the wheel . . . . . is to be interpreted as referring to the complete sequence inversion, removal of the wheel, re-inversion of the wheel remote from the man, and addition of the wheel rather than just . . . . . . inversion . . . . . but if the did not then the vertical angular momentum of the two masses becomes $4L_{\rm W}$.
