Norman Del Mar writes in Richard Strauss:

This group of Vier letzte Lieder was never heard by Strauss himself, nor did he give a clear indication of the order in which they were to be presented, whereas there was never any doubt that they must be sung by a soprano. At the end only the memory of his Pauline's voice could be his companion on these farewell excursions through the music to which his whole existence had been dedicated.

The first performance was given on 22nd May 1950 by Kirsten Flagstad and the Philharmonia Orchestra under Furtwängler in the Royal Albert Hall, London, on which occasion they were sung not in chronological order but with Beim Schlafengehen first and ending naturally with Im Abendrot, September and Frühling taking the remaining places as second and third respectively.

But when during the same year they were published, the editor, Dr Roth came wisely to the conclusion that a more satisfactory as well as more logical order was:

Frühling
September
Beim Schlafengehen
Im Abendrot

and in this form they have throughout the world become beloved above all Strauss's orchestral Lieder, and rank amongst his most admired works in any genre. (Vol. 3, p.466).

In order of composition, the songs (and dates of completion) are:

I = Im Abendrot (6 May 1948)
F = Frühling (18 July 1948)
B = Beim Schlafengehen (4 August 1948)
S = September (20 September 1948)