Complex sentence: Responsibility for nominating and dismissing the prime minister (who is elected by the Riksdag) was transferred to the Speaker of the Riksdag and the prime minister appoints and dismisses his ministers at his or her sole discretion.
Split into simpler sentences: Responsibility for nominating and dismissing the Prime Minister (who is actually elected by the Riksdag) was transferred to the Speaker of the Riksdag. The Prime Minister appoints and dismisses his ministers at his or her sole discretion.