We can use the "Obj-Open" or "Obj-Open-By-Handle" method in an activity (pyWorkCover.pzInsKey to open the instance of parent case from the child case.) to open the parent case and set the data from the child case and commit the changes.
Please use updateCase smart shape to update child data into parent. That utility accept two parameter one in inskey and other is one data transform name. Prove the key value from pxCoverInsKey prop and write a dt in which set the necessary from parameterized parent page to primary page in this case primary page will be the page of your paren
There is no OOTB way to Automatically propagate Data from a SubCase to its Parent Case. You will need to write a Custom Data Transform or Activity to propagate changes from a Sub-Case to its Parent Case and then call the Custom Data Transform or Activity when you need to propagate the data back to the Parent