Twisted conjugacy in generalized Thompson groups of type F

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If ϕ is an automorphism of a group G and x,y∈ G, we say that x and y are ϕ-twisted conjugates if there exists an z∈ G such that y=z.x.ϕ(z⁻¹). This is an equivalence relation. If there are infinitely many ϕ-twisted conjugacy classes for every automorphism ϕ of G we say that G has the R∞-property. We prove that the generalized Richard Thompson groups Fₙ and F(l,A,P) have the R∞-property.