Generally speaking, a person who is a US citizen or permanent resident (green card holder) must file a US tax return and pay US taxes on all their world-wide income, even if they do not live in the US.
However, someone who is a diplomatic employee of a foreign government is usually not considered a "US resident" for tax purposes, even if they physically live in the US (because they owe their allegiance to the foreign government). That usually means they would file a non-resident tax return and only pay tax on "US-source" income. US-source income would not include his foreign salary in this case, but could include money he makes from sale of investments or property in the US.
He can probably get tax assistance from his government. There are some legal issues here that really require a more detailed discussion than this forum can provide.
