Consider two independent conducting shells (not thin shells! i.e., their internal and external surfaces do not overlap.) whose shapes of external surfaces are identical but internal surfaces are not necessarily identical. They both enclose a point charge $q$ with the same quantity and sign but they may be stationed in different positions as to the two shells. See below.
Note that in fact the two systems are completely independent (i.e., far apart), although they look "close" shown in my drawing. And of course, there is nothing else in the surroundings!
Obviously, on both shells' internal surface there will be the same quantity of induced charge $-q$, which, in turn, will induce charge $q$ on both external surfaces. Subsequently, the induced charge distributed on their external surfaces will give rise to the electric field exterior to the external surfaces.
For the two systems the only things they have in common are the shape of the external surface and the quantity and sign of the enclosed point charge. Now the question is, do they necessarily share the same electric field exterior to their external surfaces?
I know if the shells are connected to the ground the answer will be yes. But what if they are NOT connected to the ground?