  We discuss the Einstein tensor, the supercurrent and their conservation laws
of old and new minimal formulations of supergravity in the superconformal
approach. The variation of the action with respect to the gauge field of the
$R$-symmetry in the conformal approach (the auxiliary field in the
super-Poincar\'{e} action) allows to find the Einstein tensor and supercurrent
in any curved background. Hence generalized expressions for their Ward
identities follow. This proceeding is based on arXiv:1805.09228,
arXiv:1705.02272.
