Does the angular momentum of a body change when its axis of rotation changes? Why?

(A) Yes,the angular momentum of a body changes when its axis of rotation changes.
This is because angular momentum is defined as $\vec{L} = \vec{r} \times \vec{p}$.
When the axis of rotation changes,the position vector $\vec{r}$ relative to the new axis changes,and the direction of the angular velocity vector $\vec{\omega}$ also changes.
Since $\vec{L} = I\vec{\omega}$,a change in the axis of rotation alters the moment of inertia $I$ and the direction of $\vec{\omega}$,thereby changing the angular momentum $\vec{L}$.