A note on k-potence preserving maps

Let Mn be the algebra of all n×n complex matrices and Γn the set of all k-potent matrices in Mn. Suppose ϕ:Mn→Mn is a map satisfying A-λB∈Γn implies ϕ(A)-λϕ(B)∈Γn, where A, B∈Mn, λ∈C. Then either ϕ is of the form ϕ(A)=cTAT-1, A∈Mn, or ϕ is of the form ϕ(A)=cTAtT-1, A∈Mn, where T∈Mn is an invertible matrix, c∈C satisfies ck=c.