Note that the change in rate is given by the formula stated in the question, i.e., $\mathrm{dr} = \lambda \mathrm{dt} + s \, \mathrm{dw}$

However, we have been asked to find the drift of the rate and standard deviation per month, respectively.

The drift to the short-term rate is given by $\lambda \mathrm{dt}$ while the standard deviation is given by $\sigma \sqrt{\mathrm{dt}}$.
Therefore, $\lambda \mathrm{dt} = 0.239\% \times \frac{1}{12} = 0.01992\%$ and $\sigma \mathrm{dt} = 1.20\% \sqrt{\frac{1}{12}} = 0.35\%$