Begin by accessing the Robert Koch Institute (RKI) COVID data. The RKI provides public access to their datasets, often via CSV or API endpoints. Visit the RKI COVID data web page or documentation to locate the URL or endpoint where the data is hosted.

Use a programming language such as Python to download the data. Utilize libraries like `requests` for APIs or `pandas` for CSV files. For example, if the data is in CSV format, you can use:
```python
import pandas as pd
data_url = 'your_rki_data_url.csv'
df = pd.read_csv(data_url)
```

Once the data is downloaded into a DataFrame (e.g., using `pandas`), inspect it to understand its structure. Clean the data by handling missing values, correcting data types, or filtering unnecessary columns. This ensures that the dataset is ready for transformation into JSON.

After cleaning, transform the data into the desired structure that fits the JSON format. Modify the DataFrame to match the hierarchy and keys you want in your JSON file. You may group, summarize, or restructure the data as needed.

Use the DataFrame's method to convert it directly to a JSON object. In `pandas`, you can easily achieve this using:
```python
json_data = df.to_json(orient='records')
```
This converts the DataFrame into a JSON string with each row being a JSON object within a list.

Write the JSON data to a file on your local system. Use Python's built-in `open` function to create a new file and write the JSON string into it:
```python
with open('rki_covid_data.json', 'w') as json_file:
json_file.write(json_data)
```
This will save the JSON string to a file named `rki_covid_data.json`.

Finally, verify the integrity of the JSON file by loading it back into a program and checking for errors. You can use Python’s `json` library to load and inspect the data:
```python
import json
with open('rki_covid_data.json', 'r') as json_file:
data = json.load(json_file)
print(data)
```
Ensuring the JSON file is correctly formatted prevents issues when using it in other applications or systems.

By following these steps, you can successfully move RKI COVID data to a JSON file without relying on any third-party connectors or integrations.