This question tests your ability to convert a direct statement in the simple past tense into indirect speech. When transforming "He said, 'I wrote a letter.'" into indirect speech, the primary rule to remember is the backshift of tenses.
When the reporting verb (here, "said") is in the past tense, the tense of the verb in the reported clause usually shifts one step back into the past. The simple past tense ("wrote") in direct speech changes to the past perfect tense ("had written") in indirect speech. This change indicates that the action of writing occurred before the act of reporting it.
Additionally, the pronoun "I" changes to "he" to reflect the subject of the reporting verb. The conjunction "that" is often used to introduce the reported statement, though it can sometimes be omitted. Therefore, "He said that he had written a letter" correctly applies these rules.
Option A, "He said that he wrote a letter," incorrectly retains the simple past tense. Option C uses "says," which is present tense, and option D incorrectly changes the pronoun to "I" instead of "he." The correct transformation ensures both the pronoun and the tense are appropriately adjusted for indirect speech.