Earlier this month, five Palestinian brothers were convicted in federal court of conspiring to use their Texas-based computer company to make illegal shipments of high-tech goods to Libya and Syria, two nations the State Department considers sponsors of terrorism. One of the brothers, Ghassan Elashi, the company's vice president of international marketing, was convicted of three counts of conspiracy, one count of money laundering and two counts of making false statements about the shipments. Mr. Elashi, along with two of his brothers, also faces a separate federal trial on charges relating to business dealings with Mousa Abu Marzook, the deputy...