If an LLC has always filed as an S Corp with the IRS and CA , is it necessary when changing CA entities to apply for a new FEIN for the S Corp if there is no change to the S Corp election?
The IRS requires a new EIN whenever a corporation receives a new charter from a state's secretary of state. When an LLC coverts to a corporation in California, the California secretary of state issues a new corporate charter. So the answer is yes, you need a new EIN.
Here is a link to the IRS' website with the requirements: https://www.irs.gov/businesses/small-businesses-self-employed/do-you-need-a-new-ein