There is a new Instagram feature where you can have a link to your Facebook page appear in your Instragram
One of the key limitations you have to work with in Instagram is that there is only ONE link available to you in your Instagram account - and that appears in your header profile. There are various theories on how best to use the one link, and some Instagram gurus suggest that you should update it for EVERY POST (!) so you can use it to drive customers to the right place online. As an aside, any URLs posted in the description or comments to your Instagram posts are not made into hyperlinks, likely because owner Facebook wants you to remain within their ecosystem.
But now there is a second link (on the web version of Instagram only, so far). Very recently, a new feature has appeared in Instagram, and you can put your Facebook page as an additional link in the header. To do this, go to your Facebook page, select settings and then "Instagram Adverts" and link your Instagram account to your Facebook page. This setting has previously only been used if you want to run advertising in Instagram, as there is a validation through to your Facebook Page. But now that link is being promoted further and visible in your Instagram description.
Abracadbra, as the magician says, and a link to your Facebook page appears on the next available line in your Instagram header