The answer depends on what representation is being made in the letter. The fact that is it not signed by a Virginia lawyer would not necessarily make the demand letter "authorized" or "unauthorized"
Either the client authorized the demand or he didn't . It doesn't matter who signed the letter.
If the client authorized that the demand be made and no misrepresentation is made in the letter then likely nothing is wrong with the letter.
My caveat of course is that I don't know all the facts and have not seen the letter.
Ben Glass is licensed in Virginia. He offers a number of free consumer book downloads at his site for information purposes only. You should consult an experienced, board certified attorney in your area. Obviously, no attorney client relationship is formed by participating in Avvo.