eipjoo In years to come, Harry would never quite remember how he had managed to get through his exams The main finite verb "would remember" describes a future time. " "How he managed to get through" (simple past) would not be incorrect. The past perfect is usually optional --- a tool to clarify past sequences.
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eipjooIn years to come, Harry would never quite remember how he had managed to get through his examsThe main finite verb "would remember" describes a future time. His "having managed" clearly took place prior to the "remembering."