Do I need to apply for a visa for my boss under the following travel schedule?

My boss flies from Tokyo (or poss Taipei) into Beijing the evening of 12 April. He is in Beijing for the morning of 13 April.
He then flies from Beijing to Shanghai early afternoon of 13 April.
He then departs Shanghai early morning to return to the UK.
Do we need Visas or can he do this travel under the 72-hour free transit for foreign visitors with third-country visas?
He's a British subject.