From 1956 to 1960, he directed the music teachers' seminar at the John Petersen Conservatory in Berlin-Zehlendorf, and from 1960 he worked as a lecturer for historical musicology at the Spandauer Kirchenmusikschule.
From 1959 Forchert was a research assistant at the musicological institute of the Free University of Berlin, where he habilitated in 1967 and taught until 1978.
In 1971 he followed a call to the Hochschule für Musik Detmold for a position as full professor of musicology.
From 1988 to 1997 he was president of the International Heinrich Schütz Society, which appointed him an honorary member.
On his 60th birthday a commemorative publication edited by Gerhard Allroggen and Detlef Altenburg was published.