We discuss the correlations between particles of different momentum in a superfluid Fermi gas, accessible through noise measurements of the absorption images of the expanded gas. We include two elements missing from the simplest treatment, based on the BCS wavefunction: the explicit use of a conserving approximation satisfying particle number conservation and the inclusion of the contribution from Cooper pairs at finite momentum. We expect the latter to be a significant issue in the strongly correlated state emerging in the BCS-Bose-Einstein condensate (BEC) crossover.