Global Express flight crew reported windshear and loss of aircraft control when entering a thunder cloud in cruise flight.

Narrative

Flying north on our assigned route vector over position ZZZZZ at FL450 we had adequate separation between thunderstorms per FOM. We were flying in IFR cirrus clouds with the radar tilted appropriately and at various angles to avoid thunderstorms. During a brief clearing; we noticed a towering cumulus cloud slightly above our altitude. We only had seconds before entering this embedded cumulus cloud that wasn't detected on the radar. We advised the flight attendant to be seated and seat belt on immediately; and the passenger was already seated with the seat belt sign illuminated. We did not have adequate time or turn radius to avoid the cloud. Upon entering the cloud the upward windshear caused a stall indication kicking off the autopilot. The crew worked as a team to hand fly the aircraft and manage power as the air data computer was sending both overspeed and stall indications. The aircraft voiced 2 stall messages during the event and the crew maintained the necessary energy and an appropriate angle of attack as smoothly as possible to avoid overloading the aircraft. The upward wind shear caused a brief climb of 350'. The crew worked together to promptly and smoothly correct back to altitude FL450. The event lasted about 20 seconds and no injuries occurred. Identification: The crew visually saw the towering cumulus cloud with a break in the cirrus clouds seconds before encountering the cloud. Radar did not show a return on this towering cumulus cloud. The radar was showing returns on other thunderstorms in the area at various tilt angles. Cause: Flying into an undetected cumulus cloud near the equator during mid-afternoon thunderstorm development caused the event. Response: We advised the flight attendant to be seated and seat belt on immediately; and the passenger was already seated with the seat belt sign illuminated. We did not have adequate time or turn radius to avoid the cloud. Upon entering the cloud the upward windshear caused a stall indication kicking off the autopilot. The crew worked as a team to hand fly the aircraft and manage power as the air data computer was sending both overspeed and stall indications. The aircraft voiced 2 stall messages during the event and the crew maintained the necessary energy and an appropriate angle of attack as smoothly as possible to avoid overloading the aircraft. We contacted maintenance to check whether a maintenance inspection was necessary. It was determined that we flew through 'severe' turbulence and a maintenance inspection was not necessary. Bombardier does have a maintenance inspection for 'extreme' turbulence; which we did not encounter therefore; no maintenance inspection. Suggestions: Flying around the equator during the middle of the afternoon brings turbulence from widespread rapidly growing thunderstorms. Some of these towering cumulus clouds do not generate a return on the radar so teamwork and careful outside scanning techniques are needed. Aside from not flying in the equatorial region during the peak mid-afternoon thunderstorm development; there is not much that could be done differently to prevent our event or future events. This is just part of equatorial flying that takes experience to navigate safely.