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We prove that for many nonamenable groups Γ, including all hyperbolic groups and all nontrivial free products, the left–right wreath product group  ≔ (ℤ/2ℤ) (Γ)  ⋊ (Γ×Γ) is W*‐superrigid. This means that the group von Neumann algebra  L   entirely remembers . More precisely, if  L   is isomorphic with  L  Λ for an arbitrary countable group Λ, then Λ must be isomorphic with .

W*‐superrigidity for group von Neumann algebras of left–right wreath products