Simple steps to connecting your Instagram Account to your Facebook fan page,

1. Go to your Facebook page.
2. Click on Settings.
3. Select Instagram from the various options provided.
4. Click Connect Account.
5. Enter your Instagram username and password and click Log In. (Make sure that the “Allow access to Instagram messages in Inbox” is toggled on).
6. Click Continue a couple of times through the walk-through content.
7. Select Log in.
8. On the success message, click Continue.

Note: you must, first of all, have an already existing Instagram business account and a Facebook Fan page (or you are an admin of the Facebook fan page) to achieve this.