The validity of the J-shift or the energy-shift approximation is investigated numerically by taking the reaction O(P-3) + HCl --> OH + Cl as an example. The approximation based only on the results of J (total angular momentum quantum number) = O, which is the ordinary J-shift approximation, cannot reproduce the exact reaction dynamics well, especially when the initial rotational quantum number is high. The reaction rate constants for specified initial rovibrational states are over- or underestimated depending on the initial state and temperature. The good agreement with the accurate result of the thermal rate constant seems to be rather accidental because of the cancellations of these over- and underestimates. An extended J-shift approximation is proposed, in which accurate calculations should be carried out up to J = j(i) with \Omega\ less than or equal to Omega(max) when j(i) less than or equal to Omega(max), or up to J = Omega(max) when j(i) > Omega(max), where Omega(max) is the maximum of the absolute values of the body-fixed projection quantum number Omega that give noticeable contributions to the reaction dynamics. When the maximum J required to have a well converged cross-section and rate constant is much larger than j(i), it is recommended to carry out accurate calculations at some representative J values and to use these values to estimate probabilities at other J values by an appropriate interpolation or extrapolation procedure.