It is probably possible through Facebook APIs, however, I’m not aware of any WordPress content restriction plugins that will help you out here.
It’s probably not enough of an in-demand feature for a plugin developer to justify building it.
I understand this is a far cry from exactly what you’re looking for, but you could set up content restriction on your WordPress site with a free plugin like Paid Memberships Pro, then distribute a coupon or secret URL or something to the Facebook Group members so they can register for free.
It would be kind of a pain to keep up with if people frequently leave the group, as their membership would have to be manually revoked (assuming you don’t want people who leave the group to have ongoing access to private content on your site).
Unfortunately that’s the only idea I can think of to get something passable up and running quickly and easily, without having to spend a ton of money on a custom developed solution.
Maybe somebody else on this forum has a better idea.
Best of luck! ??