Angular momentum needn't always change in multiples of $\hbar$? I read the following claim in Slichter's popular book, Principles of Magnetic Resonance (after Fig. 4.3, it's p100 in the 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?
 A: The difference between the whole system properties and its constituents can be explained on two-particle system. Consider positronium (electron+positron) in the state $l=1$. The quantum number $l$ describes the relative motion of constituents. This state has a magnetic moment, which belongs to the whole system.
But when you consider the angular momentum operator of one particle in this system, for example, that of the electron, it is uncertain: it is equal to $\mathbf{l}/2+\mathbf{\delta}$, where $\mathbf{l}$ is the total angular momentum and $\mathbf{\delta}$ is a fluctuating part. The latter part fluctuates due to coupling to the other particle. Similarly, the positron angular momentum operator equals $\mathbf{l}/2-\mathbf{\delta}$ and is uncertain too. The expectation value of $(l_z)_{\rm{e}}$ is $\hbar/2$, but it is not an eigenvalue!
The sum of operators is not fluctuating thanks to compensation of fluctuating parts. The same reasoning is valid for the "magnetic moments" of constituents.
Generally a coupled constituent is in a mixed state, so its quantum numbers have certain expectation values, but have no eigenvalues.
