I'm sorry for your loss. Unfortunately, you cannot sue the SSA. Documents held by SSA are government records and are required to be made public under the Freedom of Information Act. The social security numbers of deceased individuals are published in the Social Security Death Index. The fact that someone committed identity theft with respect to your deceased son's social security number is not legally the fault of the SSA.
You can read about the Social Security Death Index at the link below.
Not legal advice as I don't practice law in Idaho. It's simply my two cents on the facts you describe in light of general principles of law. If you need legal advice, please consult a lawyer who holds Idaho licensure.