He said, “I am writing a letter.”

This question effectively assesses your knowledge of transforming direct speech into indirect speech, a fundamental concept in English grammar. The key rule here involves the backshift of tenses when the reporting verb, 'said,' is in the past tense. In the original direct speech, "I am writing a letter," the verb 'am writing' is in the present continuous tense. When converting to indirect speech, this tense must shift backward to the past continuous tense, becoming 'was writing.' Furthermore, the pronoun 'I' must be changed to 'he' to correctly reflect the subject of the reported statement, as 'he' is the one who originally said it. The conjunction 'that' is typically introduced to link the reporting clause with the reported clause, although its omission is sometimes permissible. Option A, 'He said that he was writing a letter,' perfectly adheres to all these grammatical transformations. It correctly changes the pronoun, shifts the tense from present continuous to past continuous, and appropriately uses the conjunction, thereby providing the accurate indirect speech rendition of the original sentence.