write something back to someone
to write a letter answering someone. I wrote an answer back to her the same day that I received the letter. Will you please write something back to Julie? She complains that you are ignoring her. I wrote a letter back to Harry, explaining what had happened.
write back to someone
to write a letter to someone in return for a letter received from someone. I wrote back to her at once, but I have heard no more from her. Please write back to me when you have a chance.