Just conservation of momentum... there's never any leftover momentum or momentum going missing under any conditions.
with two colliding objects A and B it's clear that A is pushing on B for the same amount of *time* that B is pushing on A
also the force A exerts on B is the same magnitude as the *force* B exerts on A (Newton 3rd law)
Impulse is the product of force and time so the impulse is the same magnitude