This paper investigates a proactive eavesdropping scenario, where a legitimate unmanned aerial vehicle (UAV)-enabled eavesdropper aims to eavesdrop on multiple suspicious communication links with the help of a spoofing relay. Each suspicious link comprises of a mobile source and a fixed destination. The full-duplex spoofing relay receives suspicious information and amplify-and-forwards (AF) it to the eavesdropper and suspicious destinations. To maximize the long-run eavesdropping rate, we jointly optimize the precoder at the spoofing relay, the receive combiner at the eavesdropper, and the UAV's moving trajectory. Considering the difficulty of joint optimization, we decompose the optimization into two parts, where a semi-definite relaxation (SDR)-based approach and a low-complexity solution are proposed to optimize the radio actions (the precoder and receive combiner), while the moving trajectory of UAV is learned by reinforcement learning (RL). Numerical simulations demonstrates the superiority of proposed method over other benchmarks in various experimental setups.