The phrase "to write a reply" means to compose a message or response in written form as a reaction or answer to something that was previously said or received.
Sentences with «to write a reply»
He was soon boasting of writing the reply to such stuff not in three days, but one. (religion-online.org)
I would let a good friend write her a reply I know if this happened to my friend, I would be furious and wanting to write her something. (skepticalob.com)