To correctly report your unemployment benefits you need the Form 1099-G from the state. The 1099-G will have the FEIN on it. On the 1099-G form it's called "Payer's TIN," not FEIN.
Some states do not mail the Form 1099-G. You have to access it on the state's unemployment web site. Check the state's web site or call the unemployment office to find out how to get your 1099-G.
