The correct answer is: D. No error
The sentence is grammatically correct. The word “and” is used to join two independent clauses, which are clauses that can stand on their own as sentences. In this case, the two independent clauses are “The method suggested in the lecture enables a student to learn more quickly” and “The method suggested in the lecture enables a student to have remembered for a longer period of time.”
The word “to have remembered” is a perfect infinitive, which is used to express an action that has been completed or that will be completed in the future. In this case, the perfect infinitive is used to express the idea that the student will remember the information for a longer period of time after using the method suggested in the lecture.
There is no grammatical error in the sentence.