What I would do is not include the foam eyebrows on the foam head. Cover the head in fur, then make the eyebrows separately in foam and have some wire running through them and have two long pieces of it sticking out of the back of the eyebrow (the part that will be up against the head). Then cover the eyebrows with fur and insert the wires through the head; bend and glue them down inside the head to secure the eyebrows in place.
This makes it easier to cover the puppet and makes it possible to pose the eyebrows too.