Air Berlin USA was founded in 1978 as an 100% subsidiary of the US agriculture company Lelco. The president was Kim Lundgren (maybe related to the owner of this site?
), who was a PanAm pilot if I remember right. General Manager was the former Berlin Manager of Modern Air, John McDonald. In 1979 the airline began charter flights out of Berlin-Tegel, using two ex TWA Boeing 707. Later a 737-200 was employed as well as some 737-300 and 400.
After the German reunification on 03 October 1990, German airlines were able to serve West Berlin for the first time since 1945. At the same time the special rights (cabotage) which the Allied carriers had in Berlin were reduced and eventually removed. In order to stay in Berlin, Air Berlin USA had to become a German company, which took place in November 1991.
You can find a lot more information in the book "Luftbrücken nach Berlin" from Hans von Przychowski as well as "Der deutsche Luftverkehr 1955-2000" from Karl-Dieter Seifert.