In this Note we treat the problem of resonance absorption in a heterogeneous lattice cell using Fourier transforms. It is shown that the slowing down equations for the fuel and moderator flux, resulting from a flat flux approximation and the rational approximation for the fuel escape probability, get decoupled in the Fourier transform space. This decoupling is achieved without using the normal assumption of narrow resonance approximation for the moderator collision integral, and hence can be viewed as a generalization of the equivalence theorem of resonance absorbtion theory. Using certain ideas from the theory of distributions, we obtain a Fredholm integral equation (FIE) in the transform space. This integral equation with the kernel having a pole at the origin is similar to that obtained in the Fourier transform method for the homogeneous medium problem developed in our recent work. It is shown that the tem-perature-dependent resonance integrals and Doppler coefficients can be evaluated by converting the FIE to a matrix equation using the composite trapezoidal rule. Numerical results are presented to demonstrate the accuracy of the method.