Magnetic field question

This is a problem from Reitz-Milford-Cristy-Problem 9.15(fourth Ed.) , I know the answer but I do not know how to justify it.There is a long wire carrying a current "I" above a plane,inside the plane we have to cases a)μ=∞; and b)μ=0. We must find the field above the plane. To solve the problem we split the field sources: 1)wire + 2)Magnetic plane. Part 1) is already known and to find 2) we put H=-grad∅ and solve laplace equation Δ∅=0. To solve the problem we consider an image current in case a) it is a parallel current and in case b) it is an antiparallel one.
I understand case b), in this case we have B=0 inside the plane so the normal component of H must vanish so the normal derivate of ∅ must cancell that of "I" and problem is uniquely solved.
However in case a) we have H=0 and the tangencial component of H must vanish, we can do this with a parallel image however in this case what we know is the tangencial derivate of ∅ and unicity theorem for laplace equation does not apply.
Can someone shed some light on this?(I hope my english is understandable)

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