I think we are all amazed by the 138 gallons quoted by Green-dot, thanks for a very informative post.
Could you please explain the working of the centre jet pumps. As operating crew on the aircraft in question the only control of the fuel leaving the centre tank is the two centre tank pumps (via their switches on the overhead fuel panel). As has been quoted before these (due to the attitude during cruise) stop feeding (uncovered) with roughly 900 kgs still remaining in the tank.
This 900kgs remains there until the wing tanks drop below a certain figure where the jet pumps remove it from the centre tank and pump it into the wing tanks. No annunciations on EICAS of the commencement or completion of this fuel transfer.
I think we can assume that the investigators are looking at how often the "water in tank maintenance message" has occurred on other aircraft.
Let us assume for a moment (and there is no reason tho think it was not working properly) that the message was correct having being flagged up on the last two sectors. My thought is, with this 138 gallons settled at the back of the centre tank (cruise attitude) the water would have remained there when the centre tank stopped feeding with 900kgs still in the tank.
In "normal" operation (without any water present) the centre tank (as covered above) is emptied automatically later in the cruise. Perhaps this 138 gallons of water which, sitting at the back of the tank had frozen. Normally it would have thawed during the descent and the jet pumps picked it up (I never in six years saw any "fuel" left in the centre tank on shutdown so the automatic system obviously works well). But, and it is a big but the report suggests the temperatures in Beijing were around minus 7 centigrade (on the ground) so there would have been no melting of any ice prior to arriving at Beijing. Hence it may have still been in the tank in the form of a sheet of ice.
After refuelling the maintenance message reoccurred regarding this 138 gallons of water. Even if it had thawed with the introduction of "warmer" fuel during refuelling (no mention made in the report of the actual fuel temperature available at Beijing but the OAT was minus 7C) this large quantity of water could have either remained frozen, or re-froze during the return sector.
It would have remained frozen until descending into the warm airmass around the UK, but with the attitude during the descent and initial approach being nose down (even during the "one hold" at LAM the report states that the aircraft was descending) the first time the jet pumps may have been able to pick up this water, all 138 gallons, was when following flap extension and speed reduction on the ILS glidepath (the perfect continuous descent) when the attitude increased above zero.
Experts in the layout of the pickup points of the centre jet pumps, and I appeal to the better knowledge of Green-dot, might enlighten us as to whether a thawed amount of water in the centre tank could have been transferred to, and then picked up, by the wing booster pumps then feeding it onto its associated engine once the aircraft attitude increased above zero during the final approach.