No, AZ does not have an inheritance tax.
Please note that he does do not need to report or claim an inheritance on your income tax return. Inherited money is not considered taxable income by the IRS and no reporting requirement is necessary.
However, if he inherited property and then sold it, he would need to recognize any capital gain (or loss if not personal use property) on the increase (or decrease) in the value of the property from the date of inheritance until the date sold.
Additionally, an inherited IRA (reported on Form 1099-R) will be considered taxable income. He will only pay taxes on any distribution of prior year tax-free contribution made by the decedent.
Also, if this is a foreign inheritance, there may be additional filing requirements required to report this foreign inheritance to that IRS. Only foreign inheritance or gifts over a certain amount threshold would require a Form 8938 - Statement of Specified Foreign Financial Assets and/or a Form 3520 - gift or inheritance from a foreign person (nonresident alien) or from a foreign estate and the total amount during the year exceeds $100,000.