C550 CREW HAD RWY INCURSION AT BOS.

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I WAS SIC ON A CHARTER FROM BDR TO BOS. AFTER LNDG ON RWY 4R; THE PIC INSTRUCTED ME HE WAS EXITING THE RWY ON TXWY Y. TWR INSTRUCTED US; AFTER EXITING ON TXWY Y; TO CONTACT GND. AFTER CLRING RWY 4R; I CALLED GND; ADVISED THEM WE WERE CLR OF RWY 4R ON TXWY Y. GND INSTRUCTED US TO TAXI ON TXWY Y AND HOLD SHORT OF RWY 33R. I READ BACK INSTRUCTIONS TO GND CTL AND TO THE PIC. PIC THEN READ BACK TAXI INSTRUCTIONS TO ME. THEN GND CTL CLRED US TO JOIN RWY 33R AND HOLD SHORT OF RWY 4L. I READ BACK CLRNC TO GND CTL AND TO THE PIC. THE PIC THEN READ BACK TAXI INSTRUCTIONS TO ME (CONFIRMATION). AS WE WERE TAXIING ON RWY 33R COMING UP TO RWY 4L; THE PIC STARTED TO APPLY THE BRAKES AND THE PLANE BEGAN TO SLOW DOWN. I GLANCED DOWN AT THE ARPT DIAGRAM TO CONFIRM OUR POS AND THE POSSIBLE RTE TO THE FBO ON THE FIELD. JUST AS I LOOKED UP; THE PIC WAS COMING UP TO RWY 4L AND HAD NOT COME TO A FULL STOP. JUST AS I STARTED TO TELL THE PIC TO STOP; GND CTL INSTRUCTED US TO 'STOP; HOLD POS; STOP RIGHT THERE.' THE PIC APPLIED THE BRAKES AND WE STOPPED WITH OUR NOSE OVER THE HOLD SHORT LINE. I ASKED WHAT THE PROB WAS WITH THE PIC AND HE SAID HE WAS CONFUSED WHERE HE WAS AND THOUGHT WE WERE STILL ON TXWY Y; EVEN AFTER CONFIRMING WITH ME OUR TAXI INSTRUCTIONS. AFTER ESCORTING OUR PAX TO THE FBO; I WENT OVER INSTRUCTIONS FROM GND CTL FROM START TO FINISH TO CLR UP THE PIC'S CONFUSION. INSIDE THE FBO THE PIC HAD A TELEPHONE CALL FROM TWR CTL WAITING FOR HIM AND I WASN'T GIVEN DETAILS OF THE CONVERSATION.