Yes, the Eberspacher 802 controller is backwards compatible with older Eberspacher Airtronic D4 heater versions, ( 252113 for example ).
The 802 version will switch the heater, set temperature and allow you to use ventilation. It will not read the error memory for fault codes.
If you need a controller that will read the error memory of a D4 (providing the label has h-kit symbol) you can instead use the Eberspacher Easy Start Select - Eberspacher Espar Easystart Select Heater Controller 221000341300 | Butler Technik
The connections to the heater via an easy start select can be found here - Eberspacher Espar EasyStart Select Wiring Diagrams