LibGdx: calculating view matrix from projection

Question

I'm currently working on Google VR Sdk integration with LibGDX. As a starting point, I used this one: https://github.com/yangweigbh/Libgdx-CardBoard-Extension

However I was not really satisfied with it as it does not follow the the general project structure of LibGDX projects, so I started to refactor and move things around. So far so good, I have a demo running showing a rotating cube.

Now I wanted to add a Skybox, starting from here: LibGDX 0.9.9 - Apply cubemap in environment

The image is drawn, but does not move with head rotation like the other objects, so I looked deeper into the CardboardCamera class, especially the part about setting the projection matrix. The Skybox class from above gets a quaternion from the camera's view matrix. However this matrix is not set within the CardboardCamera class; instead it sets the projection matrix directly leaving the view matrix unchanged.

So my question now is. If I have the projection matrix, how can I either get the correct quaterion for it to be used for the Skybox or how can I calculate the view matrix so that its getRotation() method returns the correct values ? If both does not make sense, where could I get the correct getRotation() data from ?

Relevant code of the CardboardCamera class:

public void setEyeProjection(Matrix4 projection) {
    this.projection.set(projection);
}

final Matrix4 tmpMatrix = new Matrix4();
final Vector3 tmpVec = new Vector3();
@Override
public void update(boolean updateFrustum) {
    // below line does not make much sense as position, direction and up are never set...
    view.setToLookAt(position, tmpVec.set(position).add(direction), up);
    tmpMatrix.set(eyeViewAdjustMatrix);
    Matrix4.mul(tmpMatrix.val, view.val);
    combined.set(projection);
    Matrix4.mul(combined.val, tmpMatrix.val);

    if (updateFrustum) {
        invProjectionView.set(combined);
        Matrix4.inv(invProjectionView.val);
        frustum.update(invProjectionView);
    }
}