PA28 INSTRUCTOR PLT AND STUDENT HAD A RWY INCURSION AFTER THEY TAXIED IN FRONT OF A KING AIR AT FPR.

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ON AUG/SAT/03; AT APPROX XA25; MY STUDENT AND I RETURNED AFTER A XCOUNTRY CHK FLT THAT DIDN'T GO WELL. AFTER VACATING THE RWY AT TXWY B WE WERE TOLD TO TAXI ON TXWY B TO TXWY D AND HOLD SHORT OF RWY 14. AS WE TAXIED DOWN TXWY B I WAS MENTALLY REVIEWING THE FLT AND TRYING TO DETERMINE HOW BEST TO EXPLAIN THE FLT TO THE STUDENT AND WRITE IT UP IN HIS SYLLABUS. IN ADDITION; FPR GND WAS DIRECTING OTHER TFC THAT DID NOT INVOLVE US SO I RETURNED MY ATTN BACK TO MENTALLY REVIEWING THE FLT. WHEN WE TURNED ONTO TXWY D; I PLACED MY FOCUS BACK ON TAXIING SINCE WE WERE NO LONGER TRAVELING STRAIGHT. AS THE STUDENT PULLED UP TO THE HOLD SHORT LINE IT SEEMED AS IF HE WAS NOT GOING TO STOP SO I HAD TAKEN THE CTLS AND STARTED TO HOLD SHORT. I THEN ASKED MY STUDENT IF WE HAD BEEN CLRED ACROSS RWY 14. HE SAID; 'YES WE ARE CLRED.' AS I RELEASED THE BRAKE AND RETURNED THE CTLS TO THE STUDENT I ASKED; 'ARE YOU SURE?' BECAUSE I SAW A KING AIR TAXIING INTO POS TO HOLD. VERY ADAMANTLY THE STUDENT RESPONDED; 'YES; YES I AM SURE.' I ASSUMED THAT DURING GND'S INSTRUCTIONS TO THE OTHER ACFT THAT I HAD SIMPLY MISSED OUR XING CLRNC. AFTER XING RWY 14; GND CONTACTED US ON THE OTHER SIDE TO INFORM US THAT WE JUST CROSSED IN FRONT OF DEPARTING TFC. AT THIS POINT THERE WAS NOTHING I COULD DO BUT APOLOGIZE AND ASK FOR A PHONE NUMBER TO CONTACT THEM. I DON'T' THINK ANY REGULATORY ACTION IS NEEDED. I THINK BOTH THE STUDENT AND I WERE DISTR WITH A POOR PERFORMANCE THAT RESULTED IN OUR ATTN BEING DIVERTED ELSEWHERE. IN ADDITION; I; AS THE INSTRUCTOR; SHOULD HAVE VERIFIED THE CLRNC WITH GND IF THERE WAS ANY DOUBT; ESPECIALLY AFTER SUCH A POOR STUDENT PERFORMANCE. I WILL REVIEW THE RWY INCURSION INFO I RECEIVED IN THE MAIL FROM THE FAA TO REFRESH MY MEMORY. I WILL ALSO CHANGE MY BEHAVIOR TO AVOID DISTRS WHILE OBSERVING A STUDENT DURING TAXI AND BE CONCERNED WITH THE POSTFLT BRIEFING AFTER WE ARE BACK IN THE CLASSROOM.