Main Question or Discussion Point
how can it be proved that the otherside of the charged parallel plate capacitor has some charge on it
on the other sideDepends what you mean by "prove".....
In fact the charges are equal and opposite.....how about putting an ammeter on each side of the capacitor..one between the capacitor and the positive and the other between the capacitor and negative side of whatever supply you use....
You can also use Kirchoffs current law....if you accept conservation of electric charge.
If you remember that current is charge flow per unit time it may give you insight....q=it,
i = q/t.