The story
Vallensbæk is known from at least 1184 under the name Wolensbech, possibly translating to 'narrow land area' or 'the field with the brook'. In the Middle Ages, when Denmark was divided into syssels, Vallensbæk was part of Østersyssel. It later became a part of Copenhagen Fief, which was changed to Copenhagen County in 1661. Although Copenhagen County changed many times over the years, Vallensbæk always remained within the borders. When the counties were disestablished in 2007, Vallensbæk came under the new Capital Region of Denmark.
Since 1842, and until the 1970 Danish Municipal Reform, Vallensbæk was a parish municipality. It became a regular municipality with the 1970 reform, and its borders have remained unchanged since. Vallensbæk wasn't merged with any other municipality in the 2007 municipal reform.
From Wikipedia’s article on Vallensbæk Municipality, shared under CC BY-SA 4.0.5

