Forest Resources Conservation and Shortage Relief Amendments Act of 1993 - Amends the Forest Resources Conservation and Shortage Relief Act of 1990 to direct the Secretary of Commerce to: (1) prohibit through 1995 the export of unprocessed timber from State and other public lands, or the purchase of such timber as a substitute for exported private land timber; and (2) administer such prohibitions. Authorizes a State, upon approval of the Secretary, to implement a program in lieu of the Federal one. Establishes civil penalties for violations of this Act.