In the opening days of his war against Iran, Donald Trump had a message for members of the Iranian Revolutionary Guard Corps: Surrender and get “total immunity”—or face “absolutely guaranteed death.”

An elite armed force that exists outside Iran’s normal military structure, the IRGC began as the ayatollah’s personal strike force. But during the country’s reconstruction in the 1980s after the Iran-Iraq War, it also became a major economic force. The construction companies that the Guard organized became spectacularly lucrative, expanding their work abroad.

The Guard is now both the spine of Iran’s military and a driving force in its economy. And this isn’t the first time Trump has crossed paths with people with alleged IRGC connections.

Back in 2012, long before he ever was the GOP’s dark-horse presidential candidate, Donald Trump signed a deal to put his name on a sail-shaped tower in Baku, Azerbaijan—a notoriously corrupt, oil-rich city on the shores of the Caspian Sea. His partners in the deal were suspect: the family of then-transportation minister Ziya Mammadov, a man with a $12,000 annual salary but an estimated net worth in the billions.

Under the terms of the deal, Trump was set to make millions of dollars, renting his name to be used to market an already built building that had been constructed by the Mammadovs. Trump’s company would then continue to manage hotel operations at the newly christened Trump Tower Baku. The hotel never opened. (A fire later at least partially gutted the building,........

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