First, you need access to the OpenWeather API. Sign up at the OpenWeather website and obtain your API key. This key will allow you to make authorized requests to the API.

Ensure you have Python installed on your system. You will also need the `requests` library to interact with the OpenWeather API and the `google-cloud-firestore` library to interface with Google Firestore. You can install these using pip:
```bash
pip install requests google-cloud-firestore
```

Go to the Google Cloud Console and create a new project. Enable Firestore by navigating to Firestore in the side menu and selecting "Create Database." Follow the instructions to set up Firestore in Native mode.

In the Google Cloud Console, navigate to "IAM & Admin" > "Service Accounts." Create a new service account and generate a key in JSON format. Download this JSON key file and set the `GOOGLE_APPLICATION_CREDENTIALS` environment variable to its path:
```bash
export GOOGLE_APPLICATION_CREDENTIALS="/path/to/your/service-account-file.json"
```

Write a Python script to fetch weather data from OpenWeather. Use the `requests` library to make an HTTP GET request to the OpenWeather API endpoint, passing your API key and desired parameters (e.g., city name, coordinates).
```python
import requests

def fetch_weather_data(api_key, location):
url = f"http://api.openweathermap.org/data/2.5/weather?q={location}&appid={api_key}"
response = requests.get(url)
return response.json()
```

In your Python script, initialize the Firestore client using the `google-cloud-firestore` library. This will allow you to interact with your Firestore database.
```python
from google.cloud import firestore

def initialize_firestore():
db = firestore.Client()
return db
```

Using the Firestore client, create a function to store the fetched weather data into a Firestore collection. You can specify the collection name and document structure based on your requirements.
```python
def store_data_in_firestore(db, data):
doc_ref = db.collection('weather_data').document(data['name'])
doc_ref.set(data)

if __name__ == "__main__":
api_key = 'your_openweather_api_key'
location = 'London'
weather_data = fetch_weather_data(api_key, location)

db = initialize_firestore()
store_data_in_firestore(db, weather_data)
```

By following these steps, you can successfully move data from OpenWeather to Google Firestore without using third-party connectors or integrations. Adjust the script as necessary to suit your specific needs, such as handling errors or scheduling the script to run at regular intervals.