In recent years, ferromagnetic Ga(Mn)As has emerged as a highly interesting material for semiconductor spintronics. One possible application is to use Ga(Mn)As as an injector layer to inject spin-polarized carriers into a non-magnetic semiconductor heterostructure. As Ga(Mn)As layers are typically grown at much lower substrate temperatures than high-mobility GaAs heterostructures, a combination of both requires that the ferromagnetic layer is grown last. We have prepared samples by molecular beam epitaxy which consist of two quantum wells (QWs) of different widths grown at high substrate temperature. The upper QW is separated by a thin barrier (few nm) from a ferromagnetic Ga(Mn)As layer grown at low substrate temperature, while the lower QW is widely separated (more than 100 nm) from the Ga(Mn)As. We observe that the photoluminescence of the upper QW is red-shifted and partially quenched as compared to a control sample without a Ga(Mn)As layer, and time-resolved Faraday rotation measurements reveal that the spin lifetime in the upper QW is up to 50 times longer than the one in the lower QW. We attribute these observations to Mn back-diffusion into the upper QW during sample growth. Both, the PL and the Faraday rotation technique, are highly sensitive to small quantities (below 0.05%) of Mn and allow us to study the effectiveness of different types (e.g., a short-period superlattice) and thicknesses of barrier layers in suppressing Mn diffusion.