What was found
APU FIRE WARNING LIGHT ILLUMINATED IN FLIGHT. APU WAS NOT OPERATING AT THE TIME OF INDICATION; THE FIRE BOTTLE WAS DISCHARGED. AIRCRAFT RETURNED TO HNL AND LANDED WITHOUT INCIDENT. REMOVED AND REPLACED FIRE LOOP ELEMENT IAW AMM 26-15-1 FOR TROUBLESHOOTING, OPERATIONAL CHECK OK, NO FIRE WARNING WHILE THE APU IS OPERATING. REMOVED AND REPLACED THE APU FIRE BOTTLE IAW AMM 26-22-11, ELECTRICAL CHECK GOOD. AIRCRAFT RETURNED TO SERVICE.