Home Secretary Theresa May has said she is pleased Abu Hamza has finally faced justice and will spend the rest of his life behind bars "where he belongs".
She added: "His conviction was facilitated by this Government's tireless work to successfully remove him from the UK to face trial."
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Michael Carson had denied 12 counts of indecent assault and one of inciting a child to engage in sexual activity.
Charles, known as the Duke of Rothesay when in Scotland, will mark the success of The Prince’s Foundation’s programme in Cumnock, Ayrshire.
The Duke of Cambridge will appear in conversation with the broadcaster at the World Economic Forum in Switzerland.