It is possible with ExecuteScript and Groovy if you don't have a SecurityManager set on the JVM that would prevent Groovy from getting at the ProcessorNode which is a private member variable of the StandardProcessContext. The following script can be used in ExecuteScript to add the parent process group ID as an attribute to an incoming flow file:

def flowFile = session.get()
if(!flowFile) return
processGroupId = context.procNode?.processGroupIdentifier ?: 'unknown'
flowFile = session.putAttribute(flowFile, 'processGroupId', processGroupId)
session.transfer(flowFile, REL_SUCCESS)