The extended completeness relation (ECR), established in the complex scaling method, is applied to the energy levels calculated from the absorbing boundary condition (ABC) using the basis expansion technique. The strength function of the binary breakup, induced by the external dipole field, is calculated on the basis of the ABC + ECR method. The strength function calculated from ABC + ECR nicely reproduces the dipole strength obtained from the exact scattering wave function. According to the ECR assumed in ABC, the strength function is decomposed into contributions from the resonant and non-resonant continuum. The feature of the individual contributions
in the ABC strength function is completely consistent with the result reported in the study of the complex scaling method. The non-resonant continuum strength is investigated in more detail, and the integral path in the extended completeness relation in ABC is also discussed.