Export via Shopify Private App allows you to retrieve orders from other Shopify store without the need of installing Exportible app on that store.
But the other Shopify store has to create an app. Steps:
1. Navigate to Shopify Admin > Apps.
2. Click on Develop apps for your store.
3. Click on Create an app.
4. Once click on the create an app, it will pop up this. You need to enter App name and App developer email. Then, just click on Create app.
5. Then, it will direct to this page. You need to select the tab API credentials to get the API key and Password.
6. To access the tokens you should click on the Configure Admin API scopes.
7. It will direct to this page, you need to find for Orders and check the box of read_orders and write_orders. Once selected, click Save and Install app.
8. After installed the app, you can see the token, API key and secret key.
Shopify API password starts with shpat_