Moving from Munich to Cologne

Hi All,

We are an Indian couple living in Munich. My wife plans to move to cologne next month since she has a job. I will stay in Munich. My question is what are the changes she needs to do apart from Registering in the local Rathaus? Anyone has similar experience?

Address in her Blau Card will also change I guess? Will it be done from the Rathaus itself in Cologne?

What about Finanzamt? Currently she is registered in Munich Finanzamt.

Any other changes that might be necessary. Please let me know.