Sorry for any confusion on the airports.
Here is the updated information.
Flight Details:
Maui Airport is JHM (Kapalua)
Kauai Airport is LIH (Lihue)
Available Flights Between Islands:
Depart Maui 12:30pm Flight #2517 Island Air connect in Honolulu Flight#1004 Arrive Lihue 2:14pm
Depart Maui 3:27pm Flight #57 Island Air connect in Honolulu Flight #503 Arrive Lihue 5:51pm