Most tax preparers would probably refuse this request, citing IRS ethical standards. Without a written authorization to release information, there would be little defense against a malpractice suit if the landlord denies the application. Even with a release, fax is basically NEVER considered a reasonable business practice for handling confidential information because there is no control over who has access on the receiving end.
It was different in the past, but nowadays the professional approach is to hand the letter to the client personally. Period.