SHORTLY AFTER ENTERING U.S. AIR SPACE, THE PLT (A MEXICAN NATIONAL) CANCELED HIS DVFR FLT PLAN. ABOUT 9 MIN LATER, HE DECLARED AN EMERGENCY & SAID THE ENG HAD LOST POWER. DURING AN EMERGENCY LANDING AT NIGHT, THE ACFT HIT TREES & CRASHED.ACCORDING TO AN FAA FORM 337, AUX FUEL TANKS HAD BEEN INSTALLED IAW STC SA2479WE. HOWEVER, THE INSTALLATION WAS NOT DOCUMENTED IN THE LOG BOOKS; THE WT & BALANCE INFO WAS NOT REVISED & THE FUEL SELECTOR & GAUGES WERE NOT PLACARDED TO REFLECT THE INCREASED CAPACITY. THE PLT RPRTD HE WAS CHANGING FUEL TANKS WHEN THE ENG DEVELOPED A 'VAPOR LOCK' & WOULD NOT RESTART. HE STATED THE 'VAPOR LOCK' PROBLEM HAD OCCURRED ON PREVIOUS FLTS, BUT HE HAD ALWAYS BEEN SUCCESSFUL IN RESTARTING THE ENG. ADDITIONALLY, HE SAID THE PROBLEM HAD NOT MANIFESTED ITSELF PRIOR TO INSTALLATION OF THE AUX TANKS. AN EXAM OF THE TANKS REVEALED NO BOOST PUMPS OR TRANSFER PUMPS WERE INSTALLED. APRX 12.5 GAL OF FUEL WAS DRAINED FROM THE ACFT; UNUSABLE FUEL WAS 7 GAL. THE FUEL SELECTOR WAS FOUND BETWEEN THE LEFT TANK & OFF POSITIONS.