What is the ruling on opening the Mus'haf during a Quran memorization test due to forgetting the beginning of verses, while feeling guilty?

You must repent to Allah Almighty by regretting the sin, abandoning it immediately, and resolving not to return to it.

If the sin does not involve financial rights owed to Allah or to people, then nothing more than that is required.

You must repent from cheating on exams, and refrain from it in the future, and enter the university with repentance, for Allah accepts repentance from His servants and pardons evil deeds.

As for the fear that "what is built upon falsehood is false," this is a whisper from Satan that must be ignored.