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This is part II of a two-part paper that explores efficient anti-jamming system design based on message-driven frequency hopping (MDFH). In Part I, we point out that under disguised jamming, where the jammer mimics the authorized signal, MDFH experiences considerable performance losses like other wireless systems. To overcome this limitation, we propose an anti-jamming MDFH scheme (AJ-MDFH), which enhances the jamming resistance of MDFH by enabling shared randomness between the transmitter and the receiver using an AES generated ID sequence transmitted along the information stream. In part II, using the arbitrarily varying channel (AVC) model, we analyze the capacity of MDFH and AJ-MDFH under disguised jamming. We show that under the worst case disguised jamming, as long as the secure ID sequence is unavailable to the jammer (which is ensured by AES), the AVC corresponding to AJ-MDFH is nonsymmetrizable. This implies that the deterministic capacity of AJ-MDFH with respect to the average probability of error is positive. On the other hand, due to lack of shared randomness, the AVC corresponding to MDFH is symmetric, resulting in zero deterministic capacity. We further calculate the capacity of AJ-MDFH and show that it converges as the ID constellation size goes to infinity.