Machine learning for missing data in time series
If column B truly exhibits the same patterns, evolution, and rate-of-change as column A, then that means the values of column B are just a translation of A.  That is, $B_i = A_i + c$, where $c$ is some constant.

If this is the case, then you don't need machine learning to impute values.  Knowing $A$ is just as good as knowing $B$.  You just need to estimate $c$.  One good way to estimate $c$ would be to compute the mean difference between $B$ and $A$.

On the other hand, if B is related to A, but does not exhibit the exact same patterns and rate-of-change, then machine learning might be a little more appropriate.  You'll want to train a regression model that predicts B as a function of A, then use the model to fill in missing values of B.

Given the degree of coupling you describe between A and B, linear regression is probably a good place to start.  You can experiment with higher-order polynomials (quadratic, cubic, etc) if linear regression doesn't get the job done.  An easy way to get started would be to experiment with polynomial regression in Excel or Python.