Gouli
Certainly there was inadequate briefing here between the pilots. I think the AAIB were probably being a bit generous in suggesting there might have been more briefing before the flight that was not picked up by the CVR - even if so, a departure in these conditions should have had a recap just before lifting off running through particularly how high the HP would climb before pitching X degrees nose down or whatever, and who was on instruments and who if anyone was attempting visual references. Though to my mind both sets of eyes should have been on instruments in these conditions anyway. But then of course many private/corporate flights are SP anyway, though a mental brief by the pilot should then have happened.
But I'm afraid the truth is the fundemental cause of this accident was the pilots' inability to safely climb vertically solely with reference to instruments. As Crab says it is not a hard technique, but it does require familiarity and justifiable confidence. Once on the way up there is no way out if it goes wrong, and I strongly suspect the captain started to get disorientated early in the climb, panicked a bit, and then started to pitch down to get forward speed and increased stability too soon. He then got ever more disoriented with the big pitch changes and couldn't register the big picture from whatever scan he was doing.
Training on this technique is vital, but the skill can be practiced anytime, by climbing vertically, looking only at the instruments, in day VMC conditions. It's actually not that hard, providing, as with all hand instrument flying, control inputs are small and even small deviations from target pitch and roll are corrected early.