At 1 h 55, the Captain woke the second co-pilot and said "[…] he’s going to take my place".
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Between 1 h 59 min 32 and 2 h 01 min 46 , the Captain attended the briefing between the two co-pilots, during which the PF said, in particular "the little bit of turbulence that you just saw […] we should find the same ahead […] we’re in the cloud layer unfortunately we can’t climb much for the moment because the temperature is falling more slowly than forecast" and that "the logon with Dakar failed". The Captain left the cockpit.
From a human factors point of view, I'm with you on that.
How can a guy be woken up at 1:55 and at 2:02 be in charge (albeit as PNF) of the A/C, whatever the briefing he has been given ?
When s..t hits the fan 8 minutes later, I am pretty sure that the poor guy was not totally up to speed.