The correct answer is A. let him off.
The policeman stopped the man for jumping the red light, but he did not give him a ticket. Instead, he let him go. This is an example of the verb “let off,” which means to forgive or excuse someone from a punishment.
The other options are incorrect because they do not convey the same meaning. Option B, “let him through,” means to allow someone to pass through a barrier or obstacle. Option C, “let him by,” means to allow someone to pass by without stopping. Option D, “No improvement,” is incorrect because the sentence is already grammatically correct.