code: @Override
    public void recordTaskAssignment(TaskEntity task) {
      ExecutionEntity executionEntity = task.getExecution();
      if (isHistoryLevelAtLeast(HistoryLevel.ACTIVITY)) {
        if (executionEntity != null) {
          HistoricActivityInstanceEntity historicActivityInstance = findActivityInstance(executionEntity, false, true);
          if (historicActivityInstance != null) {
            historicActivityInstance.setAssignee(task.getAssignee());
          }
        }
      }
    }
docs: /*
  (non-Javadoc)
  
  @see org.activiti.engine.impl.history.HistoryManagerInterface#recordTaskAssignment (org.activiti.engine.impl.persistence.entity.TaskEntity)