Are the parallel axis theorem and the Koenig theorem for angular momentum linked with each other in rigid body dynamics?
The parallel axis theorem states that $$I_{z}=I_{cm}+ma^2$$
Koenig theorem for angular momentum states that $$\vec{L}=\vec{L_{cm}}+\vec{L'}$$ Where $\vec{L'}$ is the angular momentum measured in cm frame.
They are different of course but in which way are they related in rigid body description?
Is there a general proof of the fact that these two are related?