CONF iture,
Indeed he suggests (most likely poor editing of the article) the PF initiated the climb
before A/P and A/T disconnected. He should have swapped paragraphs 3 and 4 to concur with the BEA note's sequence of events:
1. On page 1 the report sets the scene on the flight deck. The captain has gone for a rest, and has been replaced by a supernumerary First Officer. That is standard for long flights.
2. The aircraft is cruising at FL350 (35,000ft) and there are storm clouds in the area, as there always are in the inter-tropical convergence zone. The two copilots are aware of them. The pilot flying (PF) briefs the copilot who has just taken the captain's seat that they are in choppy air but cannot climb above it because the aircraft's weight and the relatively high outside air temperature means that they are about as high as the aircraft can safely go until it has used up more fuel.
3. A few minutes later the PF makes a sidestick control input which raises the nose and causes the aircraft to climb rapidly to 38,000ft. There was no reason to climb, the PF did not announce an intention to do it, and the aircraft was not cleared by ATC to do so. The natural result of climbing without an increase in power is a loss of speed. But we'll deal with that shortly.
4. The problems for the pilots began when the autopilot(AP)/autothrottle (AT) disconnected. The disconnect occurred because there was a temporary disagreement between two independent airspeed sensors (pitot tubes) about what speed the aircraft was flying at. When there is a disagreement between two inputs to the flight control computers, the computers do not adjudicate, they abdicate control to the pilots.