Graphical User Interface (GUI) testing is one of the primary quality assurance methods for mobile apps. Manually constructing high-quality test cases for GUI testing is costly and labor-intensive, leading to the development of various automated approaches that migrate test cases from a source app to a target app. Existing approaches predominantly treat this test migration task as a widget-matching problem, which performs well when the interaction logic between apps remains consistent. However, they struggle with variations in interaction logic for specific functionalities, a common scenario across different apps. To address this limitation, a novel approach named ITeM is introduced in this paper for the test migration task. Unlike existing works that model the problem as a widget-matching task, ITeM seeks a novel pathway by adopting a two-stage framework with the comprehension and reasoning capability of Large Language Models: first, a transition-aware mechanism for generating test intentions; and second, a dynamic reasoning-based mechanism for fulfilling these intentions. This approach maintains effectiveness regardless of variations across the source and target apps’ interaction logic. Experimental results on 35 real-world Android apps across 280 test migration tasks demonstrate the superior effectiveness and efficiency of ITeM compared to state-of-the-art approaches.