Ex-Commando Graham Ellis was fighting in June 1982 when he and other marines were ordered to remove ID tags from dead Argentine soldiers so that the Red Cross could identify them.
His patrol then came under fire and he forgot about the tag in his pocket, only discovering it on his way back to the United Kingdom.
Mr Ellis, 53, who lives near Dundee, found that it belonged to Assistant Sergeant Ramon Gumersido Acosta.
He hoped to return it to mark the 30th anniversary of the war in 2012 but was unable to trace Sergeant Acosta’s loved ones.
Now – after reading about Mr Ellis on the internet – a comrade of Sgt Acosta’s, Jose Martin Ostuvald, has made contact on behalf of his fallen friend’s family.
Mr Ellis said he was now relieved that the tag could finally be returned to Sgt Acosta’s relatives, even after so many years.
“While it has no intrinsic value, it is very symbolic,” he said.
“I look forward to returning it to Sgt Acosta’s family.”
Sgt Acosta, who was 42 when he died, was a member of Special Troops Company 601, an elite corps – the Argentinian equivalent of the SAS.
Following his death, he became a national hero and was posthumously awarded “La Nacion Argentina Courage in Combat” medal.
He had a street named after him in his home town of Jesus Maria.
Mr Ostuvald said: “Ramon Gumersido Acosta was an outstanding member of the National Gendarmerie Argentina.
“For all families of fallen soldiers at war, retrieving items that belonged to them is an act of high sentimental value.
“His family and all his comrades deeply wish it [the tag] to be returned.
“We are very grateful to Mr Ellis.”
The action in which Sgt Acosta lost his life – the Battle of Two Sisters – took place during the advance towards the Falklands capital, Port Stanley.
At the time, Mr Ellis was a member of Arbroath-based 45 Commando, which led the attack, targeting Argentine positions on the well-defended Two Sisters mountain ridge.
Sgt Acosta was killed by mortar fire.
Mr Ellis has previously said: “I have a great degree of respect for this man for staying and fighting.
“Even way back then I knew he was obviously a professional and not like the young conscripts who ran away.”
The Falklands conflict began on Friday, 2 April 1982, when Argentina invaded, and it lasted for 74 days.
The conflict ended with the Argentine surrender on 14 June 1982, returning the islands to British control.
In total, 907 were killed, including 255 British servicemen and three female Falkland Island civilians.
There were 1,188 Argentine and 777 British non-fatal casualties.