Channel State Information (CSI)-based Physical Layer Authentication (PLA) is typically a promising strategy for wireless security. However, existing algorithms fail to transfer across various scenarios and immunize against attacks forging CSI. To improve the transferability and immunity of PLA, we propose a PLA enhancement framework to analyze, enhance, and assess authentication. Firstly, we provide a theoretical analysis method to discover the factors affecting the transferability and immunity of PLA. Secondly, inspired by the above discovery, an enhanced PLA algorithm is developed based on the channel time-varying pattern. Finally, we theoretically assess the scenario transferability and provide a closed-form expression for the bypassing condition of authentication. Furthermore, experimental results validate the practical applicability of our theoretical insights.