Power-series extension formula for absorbing numbers

Let $R$ be a ring, let $X$ be an indeterminate over $R$, and let $I$ be an ideal of $R$. Define

$$\omega_R(I)=\min\{n\colon I\text{ is an }n\text{-absorbing ideal of }R\}.$$

Power-series extension conjecture. For every ideal $I$ of $R$,

$$\omega_{R[[X]]}(I[[X]])=\omega_R(I).$$

This is a power-series analogue of the Anderson–Badawi formula. In the source, the formula is proved only under additional hypotheses, including the settings established in the surrounding theorems and corollaries; no general resolution is given.