Airbus has recently started reacting to the demand from the coal face for more information about the AFCS. There are some excellent Flight Operations Briefing Notes (FOBN) for the AFCS on Helionix types. It's the manual that should have come with the aircraft in the first place. However we have still had to put in a form you can actually deliver in a classroom and we still have to add stuff from the FLM, the original (mostly rubbish) training manuals and things we have found out ourselves.
I remember on a slightly earlier variant of the airbus AFCS on a different type we found that there was an entirely undocumented sub mode of the AFCS that led to the roll channel adding a roll boost command to assist with rolling wings level when the stick was centred. Unfortunately in certain conditions the stick was close to centre when at significant angles of bank...the undocumented mode led to a gremlin seeming to grab the stick and roll you level. Took ages to work out what was going on!
Basically manufacturers should be putting as much as possible out in the documentation - well done Airbus for the FOBN (within the bounds of commercial sensibilities of course).