Question: When was the second most successful fighter ace of all time died who was after Erich Hartmann and before Günther Rall?

Context articles: Eddie Rickenbacker
The Blond Knight of Germany
Erich Rudorffer
Günther Rall
Werner Schröer
Gerhard Barkhorn
Jagdgeschwader 52
Erich Hartmann
Günther Schack
Jane's WWII Fighters

Edward Vernon Rickenbacker (October 8, 1890 – July 23, 1973) was an American fighter ace in World War I and Medal of Honor recipient.
 With 26 aerial victories, he was America's most successful fighter ace in the war.
 He was also considered to have won the most awards for valor by an American during the war according to the April 2017 VFW magazine in their special World War I edition.
The Blond Knight of Germany is a book by the American authors Trevor J. Constable and Raymond F. Toliver dedicated to the life and career of the German fighter pilot of World War II, Erich Hartmann.
 Originally released in the United States in 1970, it was published in Germany the next year, as Holt Hartmann vom Himmel!
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Erich Rudorffer (1 November 1917 – 8 April 2016) was a German "Luftwaffe" fighter ace who was one of a handful who served with the "Luftwaffe" through the whole of World War II.
 He was the 7th most successful fighter pilot in the history of air warfare, with 222 victories claimed.
 Rudorffer fought in all the major German theaters of war, including the European and Mediterranean Theater of Operations and the Eastern Front.
 During the war he flew more than 1000 combat missions, engaging in aerial combat over 300 times.
 Rudorffer was shot down by flak and enemy fighters 16 times and had to take to his parachute nine times.
 He distinguished himself by shooting down 13 enemy planes in 17 minutes.
 His 222 aerial victories included 58 heavily armoured Il-2 Sturmovik ground attack aircraft.
Günther Rall (10 March 1918 – 4 October 2009) was a German lieutenant-general, the third most successful fighter ace in history and later head of the West German Luftwaffe during the Cold War.
Werner Schröer (12 February 1918 – 10 February 1985) was a German World War II fighter ace who served in the "Luftwaffe" from 1937, initially as a member of the ground staff, until the end of World War II in Europe on 8 May 1945, by which time he had reached the highest ranks of combat leadership.
 A flying ace or fighter ace is a military aviator credited with shooting down five or more enemy aircraft during aerial combat.
 Schröer was also a recipient of the Knight's Cross of the Iron Cross with Oak Leaves and Swords.
 The Knight's Cross of the Iron Cross and its higher grade Oak Leaves and Swords was awarded to recognise extreme battlefield bravery or successful military leadership.
 For the fighter pilots, the grades of the Knight's Cross were also a quantifiable measure of their success and skill.
 Werner Schröer was the second most successful claimant of air victories after Hans-Joachim Marseille in the Mediterranean.
Gerhard "Gerd" Barkhorn (20 March 1919 – 8 January 1983) was the second most successful fighter ace of all time after fellow "Luftwaffe" pilot Erich Hartmann, the two people to ever exceed 300 confirmed victories.
 Barkhorn joined the "Luftwaffe" in 1937 and completed his training in 1939.
"Jagdgeschwader" 52 (JG 52) (52nd Fighter Wing) of the Luftwaffe, was the most successful fighter-wing of all time, with a claimed total of more than 10,000 victories over enemy aircraft during World War II.
 It was the unit of the top three scoring flying aces of all time, Erich Hartmann, Gerhard Barkhorn and Günther Rall.
 The unit flew exclusively with the various versions of the Messerschmitt Bf 109 throughout the war.
Erich Alfred Hartmann (19 April 1922 – 20 September 1993), nicknamed "Bubi" ("The Kid") by his German comrades and "The Black Devil" by his Soviet adversaries, was a German fighter pilot during World War II and the most successful fighter ace in the history of aerial warfare.
 He flew 1,404 combat missions and participated in aerial combat on 825 separate occasions.
 He claimed, and was credited with, shooting down 352 Allied aircraft—345 Soviet and 7 American—while serving with the "Luftwaffe".
 During the course of his career, Hartmann was forced to crash-land his fighter 14 times due to damage received from parts of enemy aircraft he had just shot down or mechanical failure.
 Hartmann was never shot down or forced to land due to enemy fire.
Günther Schack (12 November 1917 – 14 June 2003) was a German World War II fighter ace who served in the Luftwaffe from 1939 until the end of World War II in 1945.
 A flying ace or fighter ace is a military aviator credited with shooting down five or more enemy aircraft during aerial combat.
Jane's World War II Fighters is a World War II era European Theater of Operations Combat flight simulation video game set during the U.S. American termed "Battle of the Bulge" in 1944 and 1945.
 The game featured famous fighter aircraft from World War II.
 It also featured a virtual museum, where aircraft profiles, interviews with fighter pilots such as George Unwin, Günther Rall, and others could be viewed.