By extending the moment approach of Nolting (Z, Phys, 225 (1972) 25) in the superconducting phase, we have constructed the one-particle spectral functions (diagonal and off-diagonal) for the tJ model in any dimensions. We propose that both the diagonal and the off-diagonal spectral functions are composed of two peaks, This ansatz satisfies the sum rules for the first four moments of the spectral functions. Our solutions are valid for J/t less than or equal to 2.0, Our set of non-linear equations has been served self-consistently. We obtain, in addition to the classical Hartree shift, a second Hartree shift which in the end result enlarges the bandwidth of the free carriers allowing us to take relative high values of J/t and allowing superconductivity to live in the T-c-rho phase diagram, in agreement with numerical calculations in a cluster, We have calculated the static spin susceptibility, chi(T), and the specific heat, C-v(T), within the moment approach. We find that all the relevant physical quantities show the signature of superconductivity at T-c in the form of kinks (anomalous behavior) or jumps, for low density, in agreement with recent published literature, showing a generic behavior (model independence), We briefly indicate how to include correlations in the moment approach.