The nonmesonic weak decay of polarized Λ hypernuclei is studied for the first time by taking into account, with a Monte Carlo intranuclear cascade code, the nucleon final state interactions. A one-meson-exchange model is employed to describe the → Λ N → n N processes in a finite nucleus framework. The relationship between the intrinsic Λ asymmetry parameter a Λ and the asymmetry a M Λ accessible in experiments is discussed. A strong dependence of a M Λ on nucleon final state interactions and detection threshold is obtained. Our results for a M Λ are consistent with 11 Λ → B and 12 Λ → C data but disagree with observations in 5 Λ → H e .