Hints: The martingale property is preserved under optional stopping

To solve this problem you need to be familiar with the transformations as defined in section 2.1.3 in ABG, and understand what it means that the process is stopped at time \(T\). In particular, what must be true for \(H_n\) in the transformation when \(n > T\)?

You can learn more about these topics in the video linked below.