The article that the picture comes from said the plane was stripped for parts. But that would have been for the duration of the war, what happened to the fuselage after the war I don't know.
The article
http://www.thinkdefence.co.uk/2012/04/harrier-forward-operating-base-falkland-islands/ gives the wrong aircraft number, it was XZ989.
XZ989 was a Harrier GR.3 which first flew 3rd October 1981. Delivered on 27th November 1981 and lost in a crash on 6th June 1982. Short service life!
http://aviation-safety.net/wikibase/wiki.php?id=55553 says the airframe was robbed of any spare parts which presumably made it lighter and easier to be moved back to a ship and ultimately used as for Ground Instruction at RAF Gutersloh.
The nose section was intended to be used for a Recruitment tool, presumably mounted on a trailer for airshows etc.
"Suffered loss of power while landing at the Port San Carlos F.O.B. on 08:06:1982, the aircraft hitting the ***** very hard and skidding to a halt (Wg Cdr Squire, the pilot, was shaken but not injured). Damaged beyond the resources of the BDR team and used as a spares source. Moved to RAF Stanley by 18 Sqdn Chinook after the ceasefire and then flown to Wideawake aboard LTW Hercules C.1P XV298 on 20:11:1982 Transfered to Heavey Lift Belfast G-BFYU and arrived at RAF Wittering on 23:11:1982. Removed to BAe Dunsfold by 15:03:1983 for assessment but eventually classified as CAT 5. Still at Dunsfold on 10:01:1985 when the maintenance serial No 8849M was allocated it, pending transfer to RAF Gutersloh for Ground Instruction duties."
From: FALKLANDS, The Air War. by Burden, Draper, Rough, Smith, & Wilton. Arms And Armour Press, 1986.