We investigate exciton transfer and relaxation in totally asymmetric trimer modelling energy transfer from the donor to acceptor molecule through molecular medium (DMA complex). For simplicity our model incorporates only one medium molecule. We suppose the strong coupling limit of the exciton transfer in which (Coulombic) interaction between acting molecules of our DMA system is mainly stronger than the interaction of the exciton with a thermal bath. Using simplified apek's convolution-less equations in the second order in the exciton-bath interaction for the whole exciton density matrix we investigate the time dependence of the occupation probabilities of the molecules of our system. Influence of the differnece in local energies of acting molecules as well as in interaction between donor, medium and acceptor molecules are discussed. Role of the non-Markovian effects in the description of the bath is presented.