This is a vintage 1950's or 1960's Hofbrau half liter beer krug in good condition. This style was common from the 30s-70s so it is correct for WWII. It is in good condition with only light wear and minor flaws in the glaze. Marked Made in Germany on the bottom. It needs a good cleaning before use. Great item for events to help eliminate farby bottles.
This is a krug, not a stein. Stein is what English speakers and tourists say. In German a stein is a stone, and is not used to describe a beverage container.