Regression Slope and Standardization

I. In a linear regression using standardized (z-score) data, the slope of the regression line is equal to the correlation coefficient $r$, and the slope for the regression line in original units is $r \frac{s_y}{s_x}$.

II. The slope of the regression line remains unaffected by the units of measurement for the variables.

III. Once variables are standardized, the correlation coefficient is no longer needed to compute the slope of the regression line in original units.

Which of the following statements regarding regression slopes and standardization is correct?