I read the following claim in Slichter's popular book, Principles of Magnetic Resonance (after Fig. 4.3, it's p100 in thisthe newest version.). Despite the title, the author claims it in a quite general manner in terms of common quantum mechanics.
Angular momentum changing in multiples of $\hbar$ is compelling only for a complete system, e.g., an electron and another magnetic moment. Division of angular momentum change between the parts of a coupled system doesn't have to be in integral units of $\hbar$.
Any clarification or examples?