The letters from Sergeant Du Vivier recount how four soldiers went behind enemy lines in Libya 70 years ago and blew up 37 German and Italian aircraft without a single casualty.
It was seen as the moment military chiefs were "really convinced that the SAS were an effective concept," according to historian Gavin Mortimer.
Sgt Du Vivier's first-hand account was used for the first time in Mr Mortimer's book, The SAS in World War II: An Illustrated History.
In one letter to his mother according to The Times, Sgt Du Vivier wrote: "I don't know what star I was born under but it sure was a lucky one."
The soldier, who died last year, joined the SAS as one of the original recruits in 1941, after joining the London Scottish Regiment with no military experience at the start of the war.
In the SAS's first operation, 33 out of 55 of the troops were killed or captured.
But it went on to blow up 14 planes and disable 10 others in an attack on the Thamet aerodrome before the Agedabia raid in December 1941.
Sgt Du Vivier told his mother people "would probably have found it difficult to believe that the job was done by five men on foot."
He described how the men had rations of a tin of chocolate, raisins, cheese and broken biscuits as well as a revolver, blanket, string and a flask of rum.
Sgt Du Vivier received a Military Medal for his part in the raid and went on to service in France and Germany before he was shot and returned home.
Jimmy Storrie, who lives in Scotland, is now the only original SAS recruit still alive.
