UAV-enabled multi-access edge computing (MEC) is expanding possibilities for integrated space-air-ground networks, especially in the 5G era and beyond. In this scenario, tasks from mobile users (MUs) are offloaded to nearby UAVs for execution, with results returned upon completion. However, the unpredictable mobility of MUs, coupled with dynamic network conditions and fluctuating resource availability, can degrade the reliability of communication links, leading to increased delivery latency, particularly for tasks involving large computational results. To meet stringent QoS requirements, adaptive task migration across UAVs is essential to minimize latency. To address this issue, in this paper, we first investigateComputationTaskMiGration (CTMiG) problem in UAV-enabled dynamic MEC networks, focusing on joint optimization of task-serving (offloading and migration) decisions to reduce latency for all MUs. We propose the ILCTS algorithm, an imitation learning-based joint optimization method that adaptively adjusts scheduling strategies in response to environmental changes. An improved PPO algorithm is first proposed to train a policy and generate expert data, followed by generative adversarial imitation learning to imitate the data and continuously explore new ones through online learning to enhance the policy. Experimental results demonstrate that our algorithm achieves superior performance in training accuracy and average latency compared to other representative methods.