This statement is not correct. When wages fall, the short run aggregate supply curve will not move to the left. In fact, the exact opposite is true. If wages fall, the short run aggregate supply curve actually moves to the right. The curve only moves to the left if wages increase.
One of the things that determine short run aggregate supply is the level of wages. Wages are a big part of the costs that producers face when they make goods or services. In general, when the costs that producers face drop, supply goes up. When costs increase, supply decreases. This is because a drop in wages means that suppliers can create a larger amount of goods and services for a given cost. Therefore, they will be willing to produce more at each price level. This is what is at play here. An increase in short run aggregate supply is shown graphically by a movement of the curve to the right. Therefore, when wages fall, short run aggregate supply increases and the curve moves to the right.
Therefore, this statement is false.