Is an authorized user on an account for which the primary account holder has been deceased for two years responsible for paying the amounts charged?

An authorized user does not fulfill the definition of "debtor" under the Fair Credit Reporting Act. AU's are not liable for any debt they have not signed a contractual agreement for.

If the AU is the heir of a deceased person, the deceased's estate or heirs MAY have liability for their debts. This would depend upon (their state's) inheritance laws and the terms of the will.