How to Connect your Facebook Page to your Instagram Account through the mobile app

Open the Facebook application in your mobile device.
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Click the 'Menu' section on the lower right side of the screen.
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Click the Facebook page you want to connect your Instagram account to.
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From your Facebook page, click on More.

Scroll down until you reach the 'Page Controls' grouping then from there, click 'Settings'
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From the 'Settings' page, click Instagram.
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You'll now be on the 'Connect to Instagram to Get More Features' page.
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Click on 'Connect Account' and then 'Confirm'

You'll be prompted to log into your Instagram account and asked to once again 'Confirm'.