To begin, you'll need to set up API access with Stripe. Log in to your Stripe dashboard, navigate to the API section, and generate a new API key. This key is required to authenticate your requests when accessing Stripe data.

Ensure you have Python installed on your local machine. You'll need the `requests` library to interact with the Stripe API. Install it using pip:
```bash
pip install requests
```

Use the Stripe API to retrieve the necessary data. For example, to fetch customer data, you can execute a GET request. Create a Python script (`fetch_data.py`) and use the following template:
```python
import requests

STRIPE_API_KEY = 'your_stripe_api_key_here'
url = 'https://api.stripe.com/v1/customers'

response = requests.get(url, auth=(STRIPE_API_KEY, ''))
data = response.json()

if response.status_code == 200:
print("Data retrieved successfully.")
else:
print("Failed to retrieve data.")
```

Depending on your requirements, you might want to process or filter the fetched data. This could include selecting specific fields or formatting the data. Modify your script to process the `data` variable as needed:
```python
customers = data.get('data', [])
processed_data = [{'id': customer['id'], 'email': customer['email']} for customer in customers]
```

The data retrieved from Stripe is usually in JSON format. If you've processed or filtered the data, ensure it is in a JSON-compatible structure before saving:
```python
import json

json_data = json.dumps(processed_data, indent=4)
```

Write the JSON data to a file on your local machine. This allows you to store and access the data offline:
```python
with open('stripe_data.json', 'w') as json_file:
json_file.write(json_data)
print("Data saved to stripe_data.json")
```

After saving the data, confirm its integrity by loading the JSON file and checking its contents. This ensures that the data was saved correctly:
```python
with open('stripe_data.json', 'r') as json_file:
loaded_data = json.load(json_file)
if loaded_data == processed_data:
print("Data integrity verified.")
else:
print("Data integrity check failed.")
```

By following these steps, you can efficiently move data from Stripe to a local JSON file without relying on third-party connectors or integrations.