On Jul 16th 2018 the airline released a 3 page press release stating, that cockpit voice and flight data recorders have been read out successfully. The investigation so far determined that the crew climbed the aircraft at too steep a pitch
angle (angle of attack) out of Havana leading to a stall and subsequent crash. The airline reasons that therefore the grounding of the airline as well as additional examinations imposed on the airline have no legal foundation, however, Mexico's DGCA have not responded to according requests by the airline. (Editorial note: according to ICAO rules only the investigation leader, Cuba's Accident Investigation Board, is permitted to talk about the progress of the investigation, participants in the investigation including the affected airline are not permitted to talk.
Some new info after the flight & data recorders were evaluated. Could be as simple as a stall caused by to high of a pitch on departure.