I have website with like button and facebook page that was created manually. I want link these pages. So when user clicks like button, he subscribes on facebook page and he will recieve all updates in the future. How can
This would depend on if the like button is "liking" your Facebook page, or your website URL.
If it's liking your Facebook page, then the user is automatically subscribed to all those updates - just like if the user had clicked "like" on Facebook.
If it's liking your website URL then you can't make them automatically like the facebook page too.
I think, when you put like button of you FB page its linked automatically.