PA28 PLT ON TRAINING FLT AND AFTER DEPARTING OPF; IMMEDIATELY CONTACTED MIA APCH FOR FLT FOLLOWING; THEN SHORTLY CHANGE TO FLL TWR IN TIME TO BE ADVISED OF A DEPARTING LEAR.

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THE OWNER OF THE ACFT; WHO IS INST RATED; NEEDED A SAFETY PLT SO THAT HE COULD FLY 2 PRACTICE ILS APCHS TO OPF. HE ASKED ME; A PVT PLT WITHOUT AN INST-RATING; TO BE HIS SAFETY PLT. THE PLAN WAS FOR HIM TO FLY THE FIRST HALF OF THE FLT (TKOF AND 2 APCHS); THEN I WOULD FLY THE SECOND HALF OF THE FLT (A VFR CRUISE ALONG THE SHORE). AFTER DOING HIS 2 APCHS; HE WAS IN CONTACT WITH OPA LOCKA TWR. WHILE CLBING OUT EBOUND BTWN 300-500 FT; I HEARD HIM SAY TO OPA LOCKA TWR THAT HE WAS SWITCHING TO MIAMI APCH FOR FLT FOLLOWING AND THEN HE CHANGED FREQS. BUT I DID NOT EVER HEAR OPA LOCKA TWR TELL HIM TO CHANGE FREQS THAT SOON WHILE STILL IN CLOSE PROX TO OPA LOCKA ARPT. AS HE WAS CLBING; HE SAID TO ME; 'THE PLANE IS YOURS.' I TOOK OVER AS PIC FOR THE SECOND HALF OF THE PLANNED FLT AND CONTINUED CLB EBOUND WHILE HE CALLED MIAMI APCH TO GET FLT FOLLOWING. MIAMI GAVE A NEW XPONDER SQUAWK CODE; HAD ME CLB TO 1000 FT TO THE SHORE; THEN CLRED ME TO TURN N INTO FORT LAUDERDALE-HOLLYWOOD INTL AIRSPACE (FLL) AT 1000 FT. VERY CLOSE IN TO FLL'S DEP PATH; MIAMI SWITCHED ME TO FLL TWR. I CHANGED FREQS AND COULD SEE A LEARJET CLBING OUT THAT WOULD PASS ABOUT 1000 FT OR MORE OVER US. DURING NON-FLT FOLLOWING FLTS; FLL HAS ALWAYS HAD ME FLY 500 FT OR LOWER ALONG THE SHORE; SO I THOUGHT IT ODD THAT THEY HAD ME AT 1000 FT. AS SOON AS I HAD TUNED IN FLL TWR; I HEARD HIM TELL THE LEARJET ABOUT TFC (US); BUT THAT HE WAS NOT IN CONTACT WITH THAT TFC (BECAUSE I HAD BEEN TALKING WITH MIAMI AND HAD JUST SWITCHED FREQ). I IMMEDIATELY CALLED FLL TWR AND SAID I HAD THE LEARJET IN SIGHT. I WOULD NOT HAVE SWITCHED TO MIAMI APCH SO SOON DURING THE CLBOUT. IN FACT; I WOULD HAVE SWITCHED DIRECTLY TO FLL TWR AFTER OPF TWR TOLD ME TO CHANGE FREQS; BUT I WAS NOT PIC WHEN THE FREQ CHANGE TOOK PLACE.