  It is established that physical observables in local quantum field theories
should be invariant under invertible field redefinitions. It is then expected
that this statement should be true for the entanglement entropy and moreover
that, via the gauge/gravity correspondence, the recipe for computing
entanglement entropy holographically should also be invariant under local field
redefinitions in the gravity side. We use this fact to fix the recipe for
computing holographic entanglement entropy (HEE) for $f(R,R_{\mu\nu})$ theories
which could be mapped to Einstein gravity. An outcome of our prescription is
that the surfaces that minimize the corresponding HEE functional for
$f(R,R_{\mu\nu})$ theories always have vanishing trace of extrinsic curvature
and that the HEE may be evaluated using the Wald entropy functional. We show
that similar results follow from the FPS and Dong HEE functionals, for Einstein
manifold backgrounds in $f(R,R_{\mu\nu})$ theories.
