No experience but; I would take pictures of damage and repair with date option on camera. When taking delivery of repair get a list of work completed. The question for the first two years will be what stresses were induced that did not immediately become evident? Were there cracks in supports that were not obvious but later failed? Did insulation get compressed and damage ducting of AC?
Better if the tree fell so you could start fresh? The positive view is that you are getting an inspection and repair that may make the unit better than new.