Kenneth Bae, 44, who was born in South Korea but is an American citizen, has been held since November when he visited the North Korean city of Rason.
He was tried in the country's Surpreme Court on charges of plotting to overthrow the government but the exact nature of his alleged crime has not been revealed.
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The suspect, 35-year-old Willie Corey Godbolt, has been arrested and was being treated for a gunshot wound in hospital.
Mohanna Abdhou, known as Montana, was out with friends when two attackers cycled up to them and opened fire in Brent, north-west London.
The US president tweeted that Mrs May gave him "full details" of the incident during talks while he attended summits in Europe.