There is:
Adler gegen Falken.
Sonderdienste der deutschen Luftwaffe im Krieg gegen die Sowjetunion
- Manuskript 1967-
https://www.booklooker.de/B%C3%BCche...chen+Luftwaffe
The publication covers nine of the ten LwKBK for the Russian campaign.
(LwKBK7 was operating in Sicily, Africa and Greece and is not covered in this book)
In 1939, 4 Luftwaffen Propaganda Kompanien were established.
In 1940 they were renamed to Luftwaffen Kriegsberichter Kompanie.
Also in 1940 4 more LwKBK were created, bringing the number to 8 regular LwKBK.
From the improvised Fallschirm-Kriegsberichter-Zug Kassmann a Fallschirm-Kriegsberichter-Kompanie was established after the invasion of Crete.
Last, the Luftwaffen Kriegsberichter Kompanie z.b.V was created as a reserve for information hotspots.
However, this is part one 1941-1943, part two or "Band 5" I have never been able to find.
/Ian