Note that the change in rate is given by the formula stated in the question, i.e., $\mathrm{d}r = \lambda \mathrm{d}t + s \, \mathrm{d}w$

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 $\lambda \mathrm{d}t$ while the standard deviation is given by $\sigma \sqrt{\mathrm{d}t}$. Therefore, $\lambda \mathrm{d}t = 0.239\% \times \frac{1}{12} = 0.01992\%$ and $\sigma \mathrm{d}t = 1.20\% \sqrt{\frac{1}{12}} = 0.35\%$