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My question is very similar to this one.

The problem: A long thin wire carrying a current $I$ lies parallel to and at a distance d from a semiinfinite slab of iron. Assuming the iron to have infinite permeability, determine the magnitude and direction of the force per unit length on the wire. (The problem can be found here.)

So, the uniqueness theorem for Poisson's equation also applies in magnetostatics, as shown here, so we can perhaps use the method of images (as indicated above): If the current density $\mathbf{J}$ is specified in some volume $V$, and either the magnetic field $\mathbf{B}$ or vector potential $\mathbf{A}$ is specified on the boundary $S$ of the volume, then the magnetic field is uniquely determined in $V$.

However, in the above problem we are not given the magnetic field or vector potential on the surface of the slab of iron, and this confuses me. I have only ever used the method of images in electrostatics on grounded conductors, on which $V = 0$, so the scalar potential is given, and $\mathbf{E}$ is uniquely determined. In the linked question above, it is shown that the image configuration satisfies the general boundary conditions at the surface between two media. Is is not necessary to show that the image configuration(s) also produce the same value of the magnetic field at that surface? If not, then why can we appeal to the uniqueness theorem to justify the method of images?

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