Luca Salasnich and Fabio Sattin On the Convergence of the WKB Series for the Angular Momentum Operator (15K, Latex) ABSTRACT. In this paper we prove a recent conjecture [Robnik M and Salasnich L 1997 {\it J. Phys. A: Math. Gen.} {\bf 30} 1719] about the convergence of the WKB series for the angular momentum operator. We demonstrate that the WKB algorithm for the angular momentum gives the exact quantization formula if all orders are summed. (To be published in Journal of Physics A: Math. Gen.).