@coolbean --
Yes, your employer withheld Illinois taxes after you became a California resident, but that was a mistake on their part. Technically and legally, per the laws of both states, you had no Illinois-taxable income after you became a California resident. Therefore, you have no income that was legitimately taxed by both states, and you are not entitled to an "other state" tax credit from California.
As I said before, your only remedy in this situation is to seek a refund of the incorrectly withheld taxes from the state of Illinois. If Illinois is requesting a letter from your employer in order to issue a refund, then it appears the issue is between you and your employer.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
