In 2001, a 45-year-old gas-station owner from Pakistan named Shahed Hussain walked into the Department of Motor Vehicles in Albany and obtained a driver’s license using fake documents for a would-be taxi driver who paid him $1,000. Mr. Hussain was caught, faced federal charges and, to avoid deportation, began a secret career that led him to pose as a recruiter of terrorists. He continued to run a series of businesses with his family, despite bankruptcy and legal issues — including, eventually, a limousine service that repeatedly ran afoul of state inspectors. Now, Mr. Hussain’s improbable journey — from asylum-seeking immigrant...