The correct option is A Would be
Let’s examine the sentence: “I can be grateful if you could write to me about it.” The sentence implies that the speaker will be ‘grateful’ on the condition that the listener could write to him or her about it. So, the speaker will be grateful in future if the given condition is fulfilled. Hence, the helping verb of the future tense should be used here. However, this helping verb should be in agreement with the helping verb ‘could’ used in the ‘if’ clause. So, instead of ‘can,’ ‘would’ should be used here. So the correct sentence would be, “I would be grateful if you could write to me about it.” Hence, Option A is the correct answer.