I would like to add just one question.
The former question arose when trying to explain,
in a non-calculus course, why both plates
should have the same charge.
What I haven't clear is if L.Kowalski wanted
to take into account end size effects or not.
For the latter case:
In the aproximation that distance between
the plates are very small in comparition
to their size, that is, infinite area of
the capacitor, or no end effects, we have
total electrostatic influence between the plates:
No E field line will reach infinity. That
stablishes a one-to-one aplication between
charges of both plates. Charges are the
source of E, and it also dies at them.
Won't this be enough?
(I guess what your answer will be: no, but
it will be interesting to know why)