Complex sentence: After Heydrich's death in June 1942, and as the war progressed, Müller's power and the independence grew substantially; this trickled down the chain of his subordinates and led to much more independence of action.
Split into simpler sentences: After Heydrich's death in June 1942, and as the war progressed, Müller's power and the independence grew substantially. This trickled down the chain of his subordinates and led to much more independence of action.