Genetic information stored in a DNA base sequence is continuously exposed to harmful factors. It has been determined that 9 × 104 different DNA damage events occur in a single human cell every 24 h. Of these, 7,8-dihydro-8-oxo-guanosine (OXOG) is one of the most abundant and can undergo further transformations towards spirodi(iminohydantoin) (Sp). Sp is highly mutagenic in comparison to its precursor if not repaired. In this paper, the influence of both Sp diastereomers 4R and 4S as well as their anti and syn conformers on charge transfer through the double helix was taken into theoretical consideration. In addition, the electronic properties of four modelled double-stranded oligonucleotides (ds-oligos) were also discussed, i.e., d[A1Sp2A3oxoG4A5] * [T5C4T3C2T1]. Throughout the study, the M06-2X/6-31++G** level theory was used. Solvent-solute non-equilibrated and equilibrated interactions were also considered. The subsequent results elucidated that the 7,8-dihydro-8-oxo-guanosine:cytidine (OXOGC) base pair is the settled point of a migrated radical cation in each of the discussed cases, due to its low adiabatic ionization potential, i.e., ~5.55 [eV]. The opposite was noted for excess electron transfer through ds-oligos containing anti (R)-Sp or anti (S)-Sp. The radical anion was found on the OXOGC moiety, whereas in the presence of syn (S)-Sp or syn (R)-Sp, an excess electron was found on the distal A1T5 or A5T1 base pair, respectively. Furthermore, a spatial geometry analysis of the discussed ds-oligos revealed that the presence of syn (R)-Sp in the ds-oligo caused only a slight deformation to the double helix, while syn (S)-Sp formed an almost ideal base pair with a complementary dC. The above results are in strong agreement with the final charge transfer rate constant, as calculated according to Marcus' theory. In conclusion, DNA damage such as spirodi(iminohydantoin), especially when becoming part of clustered DNA damage, can affect the effectiveness of other lesion recognition and repair processes. This can lead to the acceleration of undesired and deleterious processes such as carcinogenesis or aging. However, in terms of anticancer radio-/chemo- or combined therapy, the slowing down of the repair machinery can result in increased effectiveness. With this in mind, the influence of clustered damage on charge transfer and its subsequent effect on single-damage recognition by glycosylases justifies future investigation.