Donor-acceptor electron transfer (D-A ET) through a linear molecular bridge is studied for the particular case of large electronic couplings among the molecular fragments inside the bridge. This makes it possible to choose a description in terms of extended bridge states, whereas the weak coupling of the bridge levels to the D and A centers guarantees the individuality of these terminal sites. Since fast vibrational relaxation within the D and A centers as well as within the system of bridge levels is provided, we can utilize our recently developed coarse graining description of ET (Petrov et al., J. Chem. Phys. 2001, 115, 7107). In particular, it is demonstrated that the whole ET process can be reduced to single-exponential kinetics for the electronic level populations characterized by an effective D-A transfer rate. This rate contains contributions from the overall superexchange and the overall thermally activated rate. The ratio of both contributions is calculated in the framework of the Song and Marcus model valid for a vibrational spectral density describing a single active vibrational mode. Taking reasonable parameters for the D-A ET reaction, it is demonstrated that the thermally activated mechanism can dominate the superexchange ET, even though the population of the bridge by the transferred electron is extremely small. And this dominance increases with increasing bridge length. Drawing the overall ET rate versus the number of bridge units, a novel behavior is predicted. First there is a strong decay of the rate up to a certain bridge length. But it is followed by a remarkable increase which is continued by a modest further increase or an in dependence on the bridge length. Furthermore, simple analytic expressions are given to decide which mechanism may work in a given experiment. Finally, it is underlined that ET pathways along hydrogen bonds or the key an-Lino acids in proteins are extremely favorable for the thermally activated mechanism, while the pathways along covalent bonds are generally realized via the superexchange mechanism even at a small energy gap.