  We investigate the necessary conditions for the two spacetimes, which are
solutions to the Einstein field equations with an anisotropic matter source, to
be related to each other by means of a conformal transformation. As a result,
we obtain that if one of such spacetimes is a generalization of the
Robertson-Walker solution with vanishing acceleration and vorticity, then the
other one has to be in this class as well, i.e. the conformal factor will be a
constant function on the hypersurfaces orthogonal to the fluid flow lines. The
evolution equation for this function appears naturally as a direct consequence
of the conformal transformation of the Ricci tensor.
