Your husband must continue to pay Arizona state income tax on "Arizona source income", even after moving out of state. The source of wage income is usually the state where your permanent residence is located when the income is paid, so just working for an Arizona company after your move will not make it Arizona-sourced. However, if your spouse returns to Arizona from time to time (such as for training, or mandatory on-site meetings) then any income earned while physically living or working in Arizona, even temporarily, will be considered Arizona sourced. Other common Arizona source income might include rental income (if you rented your Arizona home after moving out), or the capital gains from the sale of your Arizona home (if you sold it after you established your new permanent residence in Washington). Other income like investments or interest is only taxed in Arizona if it is paid while you live in Arizona. If you have investments, you will have to carefully review your statements to see how much of the interest, dividends and capital gains were paid before you moved.
When preparing your tax return, you will have to manually allocate your income between the states, Turbotax can't guess.
If the company will allow it, he can stop his Arizona withholding. If the company won't allow it, he will get a tax refund when he files an Arizona return showing an excess of withholding over tax owed.
