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This paper investigates a distant proactive eavesdropping system in cooperative cognitive radio (CR) networks. Specifically, an amplify-and-forward (AF) full-duplex (FD) secondary transmitter assists to relay the received signal from suspicious users to legitimate monitor for wireless information surveillance. In return, the secondary transmitter is granted to share the spectrum belonging to the suspicious users for its own information transmission. To improve the eavesdropping, the transmitted secondary user's signal can also be used as a jamming signal to moderate the data rate of the suspicious link. We consider two cases, i.e., non-negligible processing delay (NNPD) and negligible processing delay (NPD) at secondary transmitter. Our target is to maximize network energy efficiency (NEE) via jointly optimizing the AF relay matrix and precoding vector at the secondary transmitter, as well as the receiver combining vector at monitor, subject to the maximum power constraint at the secondary transmitter and minimum data rate requirement of the secondary user. We also guarantee that the achievable data rate of the eavesdropping link should be no less than that of the suspicious link for efficient surveillance. Due to the non-convexity of the formulated NEE maximization problem, we develop an efficient path-following algorithm and a robust alternating optimization (AO) method as solutions under perfect and imperfect channel state information (CSI) conditions, respectively. We also analyze the convergence and computational complexity of the proposed schemes. Numerical results are provided to validate the effectiveness of our proposed schemes.