I use Lacerte, which has a Sch S Screen that the user can fill in to generate Sch S.

Screen 52 Other State Tax Credit. 

In Lacerte, the tax credit would NOT be generated automatically based on the Wages and K-1 input for a client with your Part-Year fact pattern.  It has to be generated using the above screen with additional (e.g. double-taxed) info.

Does Proseries have a similar screen?  

One thing you may need to consider - is the move temporary?

There are special COVID rules on telecomuting for CA.  Just in case.