GA TRAINING FLC OBTAIN INCOMPLETE BRIEFING AT POINT OF DEP AND INCUR RESTR AIRSPACE AT DEST.

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I WAS THE INSTRUCTOR ON A VFR CROSS COUNTRY TRIP FROM ZZZ TO ZZZ1 THIS WAS MY FIRST TRIP TO ZZZ1; AS I JUST RECEIVED MY CFII RATING. I REVIEWED MY STUDENT'S FLT PLAN AND EVERYTHING WAS PLANNED WELL. I HAD SOME CONCERN ABOUT THE PROHIBITED AIRSPACE X ALONG OUR RTE OF FLT. SO I ASKED MY STUDENT IF HE RECEIVED ANY NOTAMS REGARDING THAT AIRSPACE. MY STUDENT'S REPLY WAS THAT HE RECEIVED NO NOTAMS FROM THE FSS BRIEFING OR IN HIS PREFLT PLANNING. THE TRIP WENT AS PLANNED AND WAS UNEVENTFUL UNTIL WE REACHED ZZZ WHICH WE WERE PASSING ALMOST DIRECTLY OVER. I TOLD MY STUDENT TO CALL ZZZ1 TWR TO LET THEM KNOW THAT WE ARE APPROX XX MI E INBND FOR LNDG. THE CTLR ASKED US TO IDENT 1200. I WAS THE SURPRISED TO HEAR THE CTLR TELL US THAT WE WERE IN VIOLATION OF PX AIRSPACE AND PLACE US UNDER VECTORS TO THE ARPT. I DID NOT UNDERSTAND WHAT WAS GOING ON UNTIL WE LANDED WITH AND THE LOCALS AS THE FBO TOLD ME THAT PX HAD BEEN EXPANDED FROM A 3 MI RING TO AN 8 NM RING WHICH PLACED ME AND MY STUDENT JUST INSIDE HE 'ENHANCED' PX AIRSPACE. I CALLED AND CONFIRMED THIS WITH THE LOCAL FSS AS WELL AS CALLING PLT DEVIATIONS AS INSTRUCTED BY THE TWR. I SUGGEST DECOMMISSIONING THE LOCATION XX INTO ZZZ3 UNTIL THE ENHANCED PX IS OVER. LOOKING BACK; I SHOULD HAVE NOT SOLELY RELIED ON MY STUDENT'S GATHERING NOTAMS; BUT SHOULD HAVE INVESTIGATED THE SIT FURTHER MYSELF; CONSIDERING THE EVENTS OF 09/11/01. I WOULD ALSO IN THE FUTURE CALL THE LOCAL FSS TO MY DEST FOR LOCAL NOTAMS AND ASK SPECIFICALLY IF THERE ARE ANY NOTAMS REGARDING AIRSPACE ALONG MY RTE OF FLT.