The wireless sensor from the Gogogate2 is not compatible with the ismartgate LITE and the ismartgate PRO. As it uses a different frequency to transmit the information.
But please note that the new wireless sensors are improved for the association with IFTTT, Alexa, Google Home and Homekit. As they detect the door opening, instead of the door opened (fully horizontal position) and closed (fully vertical position) only. They detect the vibrations of the door opening, therefore they can make the detection for IFTTT triggers more reliable.
The wired sensor is ONLY compatible with the ismartgate PRO: