I inherited millions of dollars from another country. I understand that the FBI monitors funds transfers from foreign countries. What proof do I need to show that the money I am receiving is an inheritance money and not connected to drugs or terrorism?

Hire an attorney in the U.S. to determine whether you are being subjected to some sort of a Nigerian scam.

No proof what so ever, they would have to look and see where the money came from if they wanted,

I assume you actually knew the person who died? You can deposit the money in a international bank in that nation, I am sure you would go to the funeral of a close member of your family that left you that much money anyway