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. Full definition
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)