You can fetch details of Facebook page, Facebook account(user) connected to an Instagram account using user_id.

How to get user_id?
Ans: You can use Username to User ID endpoint to fetch user_id.

Where I can find Instagram -> Facebook link endpoint?
Ans: Go to Endpoint section, select Instagram -> Facebook Link group & select first endpoint.

Response:

{
    "data": {
        "ig_id": "25025320",
        "ig_username": "instagram",
        "fb_page_id": 367152833370567,
        "fb_page_name": "Instagram",
        "page_id": 367152833370567,
        "page_name": "Instagram",
        "linked_fb_info": {
            "linked_fb_user": {
                "id": "demo",
                "name": "demo",
                "is_valid": true,
                "fb_account_creation_time": null,
                "link_time": null
            }
        },
        "fb_page_url": "https://fb.com/367152833370567"
    },
    "status": "ok",
    "message": null
}

Sometimes Instagram provide fb_page_id or page_id or both.
When Instagram account is not connected to Facebook page then you will receive empty values for fb_page_id, page_id, etc
When Facebook Profile is publicly displayed by an Instagram user then you can see those details in linked_fb_info

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