FOREIGN ACR HAD STALL WARNING ON CLB OUT OF JFK; DIDN'T MAKE TURN PER SID AND GAVE TWR CTLR SOME ANXIOUS MOMENTS AS HE ENTERED APCH CTL AIRSPACE FOR LGA.

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FOREIGN ACR; WDB; DEPARTED RWY 31L AT XB22L; ON JFK-6 SID; CANARSIE CLB. THE CRI CLB REQUIRES A L TURN E OF CRI R-039 TO AVOID LGA TFC. THE ACFT REMAINED ON RWY HDG (313 DEGS) AT LOW ALT AND I INSTRUCTED HIM TO TURN L DIRECT TO THE VOR. HE APPEARED TO START HIS TURN; AND INFORMED ME THAT HE WAS HAVING PROBS; WHICH TURNED OUT TO BE A STALL WARNING; BUT AT FIRST I THOUGHT HE SAID SOMETHING ABOUT SMOKE. HE ALSO SAID THAT HE WOULD BE RETURNING AND STOPPED HIS TURN. I ASKED ABOUT HIS INTENTIONS; AND DURING A VERY LONG RESPONSE; NOTICED THAT HE WAS HDG TOWARD AN ACFT ON HIS ILS RWY 4 APCH TO LGA. I TOLD HIM TO TURN AND HE RESPONDED WITH A REQUEST TO MAINTAIN 3000 FT. AFTER PLEADING WITH HIM TO TURN L HDG 180 DEGS; HE COMPLIED; WAS TURNED OVER TO APCH CTL AND LANDED 10 MINS LATER WITHOUT INCIDENT. WHILE THE ACFT NEVER LOST SEPARATION WITH THE LGA ARR (MY ESTIMATE IS THAT THE CLOSEST THEY GOT WAS 3 MI AT THE SAME ALT); HE DID VIOLATE AIRSPACE. (THE ACFT WAS POINTED OUT TO LGA TWR BY A CO-WORKER.) AS OF THIS WRITING; NO PLTDEV OR OTHER RPT HAS BEEN FILED DUE TO THE FACT THAT THIS WAS AN EMER SIT. ALTHOUGH I AM NOT COMPLETELY FAMILIAR WITH THE IMPLICATIONS OF A STALL WARNING IN A WDB; I DID FEEL THAT BETTER COCKPIT RESOURCE MGMNT BY THE CREW WOULD HAVE AVERTED EVEN THE POTENTIAL OF A CONFLICT. THE ACFT'S FAILURE TO FOLLOW THEIR ASSIGNED RTE COULD HAVE TURNED A POTENTIAL EMER INTO A DISASTER.