The environment induced shift of any property derived from the embedded wavefunctions obtained from any method based on Frozen Density Embedding Theory depend on (a) the approximation made for the universal bi-functional v xct nad [ ρ A , ρ B ] , and (b) the modeller-decided density ρ _B used as the only quantum descriptor for N _B electrons associated with the environment. In several previous works, a particular choice for (a) and (b) was tested and shown to yield very accurate complexation induced shifts of vertical excitation energies for chromophores non-covalently bound to their environment for such excitations which do not involve large redistribution of the electron density upon excitation (errors in the range of 0.04 eV). The present work extend the previous studies to transition moments and oscillator strengths and demonstrated the limits of the predictive power of the protocol used for transition energies. For the errors in the oscillator strengths, lie below 0.06. The role of the environment polarisation and the intermolecular Pauli repulsion is analysed in detail.