AfD becomes first far-right party to win German state election since 1945

It appears there may be some confusion in your statement. As of my current knowledge up to March 2022, the AfD (Alternative for Germany) party has not yet won a state election in Germany. Although the AfD has gained substantial support in certain areas and has seats in all 16 state parliaments, it has not governed a state. Please verify the information from a reliable source, or if you are referring to a new or recent event, I may not have the updated information.