If you moved permanently, you want to file a Part-Year return for California and New Jersey. On a part-year return you only have to report the income you earned while a resident or state source income as a nonresident- so there is no double tax income to claim a credit for. Since your broker withheld for New Jersey, you will only report the income for the time you lived in New Jersey which should result in a bigger refund, but you will have to report that same income to California and will probably owe since your broker withheld for New Jersey.