Yes, you will have to manually compute how much was earned after the September move to determine how much to report. You will pay the tax to Oregon, then when you file the New York you will get a credit for the amount you paid to Oregon (on the same income) so you are not taxed twice. Because of the states involved (Oregon and New York) your situation is a bit more complicated because not all states require the Unemployment to be reported after you move out of the state.
@jjrob94
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