Answer
See the detailed answer below.
Work Step by Step
$$\color{blue}{\bf [a]}$$
In your frame, you measured the 1-m stick less than 1 m.
And since the meter stick is moving from the left then, according to the meter stick's frame, you measured the left end first.
$$\color{blue}{\bf [b]}$$
Yes, experimenters in frame $S'$ can explain why the measurement in frame $S$ is less than 1 m. According to the principles of special relativity, when an object is in motion relative to an observer, length contraction occurs along the direction of motion as perceived by the observer.
In this case, as the meter stick moves relative to the observer in frame S, the observer in frame $S'$ experiences length contraction. This contraction causes the meter stick to appear shorter than its rest length of 1 m as measured by the observer in frame $S$. Hence, experimenters in frame $S'$ can explain the measurement of less than 1 m based on the observed length contraction phenomenon in special relativity.
