The penalties depend on what was done by or due to the false claim. It could be tax fraud, if the person falsely claiming used this as a basis to not pay all taxes or claim a refund in someone else's name. It could be theft, if he used the claim of power to take money or property from another, or fraud, if the claim was used to induce or cause someone to enter into a contract or do something; etc. The penalty depends on what is done (or attempted).