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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.