Conversational AI agents are becoming ubiquitous and provide assistance to us in our everyday activities. In recent years, researchers have explored the migration of these agents across different embodiments in order to maintain the continuity of the task and improve user experience. In this paper, we investigate user's affective responses in different configurations of the migration parameters. We present a 2x2 between-subjects study in a task-based scenario using information migration and identity migration as parameters. We outline the affect processing pipeline from the video footage collected during the study and report user's responses in each condition. Our results show that users reported highest joy and were most surprised when both the information and identity was migrated; and reported most anger when the information was migrated without the identity of their agent.