The yearly dividend paid to residents from AK's permanent fund is in the range of $1,000-$2,000, so the amount your client's estate received isn't that. It sounds more like either accrued wages paid after death or uncashed paycheck amounts that were reissued and paid to the estate.
I think this is reported on the Form 1041, and if that's where you will report it and with the 1099-misc in the SSN of the deceased, I'd show this as an assignment of income on the 1040 to be safe.