Who is the German woman heard singing briefly in the Guns of Navarone?

The singer is Lale Andersen; the song is Lilli Marleen (original German spelling).

This song was broadcast nightly from Radio Belgrade, and was a favourite of both sides.

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Actually the singer is Elga Andersen and the song is 'Treu Sein' . She sings it later live in 1962 . You can search YouTube for 'Elga Andersen Treu Sein' and listen again!

(That is, if you are referring to the haunting song from the German soldiers' radio, towards end of the movie when Capt Mallory reaches the Guns of Navarone)