I just read the entire thread but still don't understand fuel surcharge. For example, here is what I found on BA website for 1-way partner redemptions:

Taxes for SFO-HKG (either economy or business) on CX is $139.60, of which $137.10 is the fuel surcharge!

Taxes for HKG-NRT-SFO (economy, not sure about business) on JL is $429.83, of which $369.00 for fuel surcharge!

Does BA give this fuel surcharge to the partner airline (e.g. $137.10 to CX) or does it keep it?