How Do I Preserve Signed Jersey?

The best thing to do is to invest in a proper display case or frame. This would ensure that you get something with some sort of UV protection (e.g. - with an acrylic front rather than glass) and a non-acidic backing so your jersey does not stain or fade. If your shadow box is already of this quality, then that should be fine.

Another thing to consider would be getting an actual framer who can do a professional job of 'framing' the jersey. They will know how to do it best and all the little things that need to be done to ensure the best result, e.g. - the jersey not touching the front panel.

Lastly, where you display it is also important. It needs to be out of direct sunlight but also somewhere that is not damp such as your basement.

If you want to display your jersey in a frame or display case, make sure the glazing (ie acrylic or glass) filters 97% or more of UV light.  Avoid backings made out of wood since these are highly acidic.   A truly non-acidic backing would be one made from alphacellulose plant fibers or one made from cotton pulp.  The most well-known brand names for this type of mat is Crescent Select, Crescent RagMat and Bainbridge Alphamat Artcare.    Another term for this type of matboard is