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We introduce a partial-differential-equation model for rechargeable lithium-metal battery (LMB) cells whose parameter values are fully identifiable from cell-level experiments. From this model, we formulate a computationally tractable transfer-function (TF) model for use within optimization loops. A strategy is proposed for regressing the TF model to cell electrochemical impedance spectroscopy (EIS) measurements to estimate parameter values. We validate the regression using a synthetic dataset before application to a single-layer LMB pouch cell. The voltage RMSE between the fully identified model's predictions and laboratory measurements is about 4 mV for a GITT profile. We provide MATLAB code to simulate the model in COMSOL, compute cell impedance from the TF model, and perform model regression.