POTENTIAL CONFLICT WITH A CIRCLING PA23 AT 3500 FT NOTED BY AN AIRLINER PIC INBOUND ON V15; 40 NM OUT FROM HNL; HI.

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THE STUDENT AND I WERE MANEUVERING OFFSHORE WELL CLR OF CLASS B AND THE VICTOR AIRWAY PRINTED ON THE SECTIONAL CHART. WE WERE MAKING LEVEL TURNS TO MAINTAIN ALT AND CLRNC FROM CLASS B AND WERE GOING TO CALL HNL APCH AND REQUEST PRACTICE APCHS. WE WERE HDG SE WHEN I NOTICED THE AIRLINER OFF OUR R WING. HE WAS HDG SE ALSO. HE WAS ABOUT 1 1/2 MI AWAY AND 1000 FT ABOVE US. WHEN I SAW THE AIRLINER OFF MY WING; I TOLD THE STUDENT TO TURN TO THE L AND BRING US CLOSER TO THE SHORELINE. I DID NOT SEE THE AIRLINER UNTIL HE WAS OFF OF OUR WING AND AHEAD OF US AND DID NOT FEEL EITHER ACFT WAS IN JEOPARDY OF A MIDAIR. ON OUR WAY BACK TO HNL; APCH CTL ASKED US TO CALL THEIR OFFICE WHEN WE WERE BACK ON THE GND. I CALLED APCH AND THEY INFORMED ME THAT THE AIRLINER THOUGHT WE WERE TOO CLOSE. THE AIRLINER AND APCH CTL RADAR SAW US. I EXPLAINED THAT I THOUGHT ALL INCOMING HNL TFC WERE ON V15 OR S OF IT. THE CTLR SAID THEY VECTOR PEOPLE CLOSER TO THE SHORELINE; WHICH I WAS UNAWARE OF. PERHAPS THE SECTIONAL CHART SHOULD HAVE A NOTICE INFORMING PLTS OF THE INCREASED TFC IN THAT AREA; ALTS THEY'RE AT; AND TYPICAL FLT PATHS THEY TAKE SINCE THE CHART DOES NOT SPECIFY ANY OF THAT.