Hi,
A few ways to do this –
1 -You could create a sky object, and place an HDRI or other environment texture on the sky. Make the sky not visible to the camera, but visible to reflections by using a compositing tag.
2- Use a texture in the environment channel of the material for your screen
3- You could actually set up some white cards using planes around your object, and have reflective on in your material.
Mike