After days of trying to get in touch with Facebook support (incredibly helpful) we managed to find a solution and above all to correct several errors that can be generated with a wrong procedure.
Since I don't like long-winded Aranzulla-style explanations and I'm writing this article to help and not to do SEO I'll get right to the procedure:
1. The Instagram account should NOT be a professional account ( For now ) or at least should be temporarily converted into a personal account.
2. Log in to your Facebook account and from there go to the FACEBOOK BUSINESS MANAGER ( Non Business suite ) related to the page you want to link Instagram to.
3. From Facebook Business Manager connect the Instagram account, via the link on the left menu, you will be asked via a popup to login.
4. Once connected to the Facebook Business Manager log in via Smartphone to Instagram / Settings and convert the personal account to professional.
5. Now go back to Facebook, go to the page to which you want to connect the Instagram profile (Remember, you must be an administrator of the page!) In the menu on the left, select configuration and then Instagram, click on the button "connect Instagram account" log in with your credentials as soon as you are prompted and voila, you will have your Instagram account correctly connected to the Facebook page of reference!
I'll also add some notes that Facebook support sent me:
IMPORTANT: The instagram account should be unlinked from the FB page before you can assign the page to your Business Manager.
Here's how to do it:
From Facebook (pc) https://www.facebook.com/business/help/898752960195806
From IG app: https://www.facebook.com/help/instagram/1717693135113805
Please note: If you have active ads on the Page (on Facebook) these will not stop working, although it is advisable to do so.
Instead Instagram campaigns need to be stopped because if you have active campaigns it won't switch the IG account to personal.
If you are requesting to remove the Page from the Business Manager currently owning it, you will need to disconnect any Instagram Accounts linked to the Page, switching the Account to Personal. The connection can be reinstated at a later date after the Page is claimed..
Hope this helps :)