The following articles are available:
Bergsträsser, Gotthelf. “Koranlesung in Kairo,” Der Islam 20 (1932): 1-42. (pdf)
Bergsträsser, Gotthelf. “Koranlesung in Kairo,” Der Islam 21 (1933): 110-140. (pdf)
With thanks to Arno Schmitt who kindly provided the files.