The correct answer is D. Will a letter have been written by him?
The other options are incorrect because they do not use the correct verb tense. The sentence is in the future perfect tense, which is used to talk about something that will have happened by a certain time in the future. The verb “to write” in the future perfect tense is “will have written.”
Option A is incorrect because it uses the present perfect tense. The present perfect tense is used to talk about something that has happened or is happening now.
Option B is incorrect because it uses the simple future tense. The simple future tense is used to talk about something that will happen in the future.
Option C is incorrect because it uses the infinitive form of the verb “to write.” The infinitive form is used to talk about something in general, not about something that will happen in the future.