What should one do who regrets cheating when memorizing the Book of Allah, and is afflicted by obsessive doubt when trying to resume memorizing it?

Dismiss the whispers (waswas), and do not give them any heed. Whenever Satan whispers to you about cheating, turn away from his whispers. Seek Allah's help in reading and memorizing. Strive to organize your time, and frequently repeat and review what you have memorized. Keep company with righteous women who will help you in memorization, and repent to Allah for the cheating you have committed.