Image charge inclusions in the prolate dielectric spheroid

A curious property of the electrostatic image theory for the perfectly conducting prolate spheroid, introduced in 2001, is pointed out: the potential outside the conducting spheroid remains unchanged if the conductor is replaced by a dielectric spheroid with an embedded charge which coincides with the image charge for the conducting spheroid case. The present note is a generalization of the corresponding observation about the classical Kelvin image theory for the conducting sphere, made in 1988.