Terrorist Hoax Improvements Act of 2009 - Amends the federal criminal code to: (1) extend the prohibition against conveying false information and hoaxes to include false information and hoaxes about any federal crime of terrorism; (2) increase maximum prison terms for hoaxes involving a member of the Armed Forces during war; (3) expand civil liability provisions relating to expenses incurred by emergency personnel in responding to a hoax; and (4) extend the prohibition against mailing threatening communications to include threats against corporations or governmental entities (as well as individuals).