  This paper is the third of a series dedicated to the study of the Delayed
Big-Bang (DBB) class of inhomogeneous cosmological models of
Lema\^itre-Tolman-Bondi type. In the first work, it was shown that the
geometrical properties of the DBB model are such that the horizon problem can
be solved, without need for any inflationary phase, for an observer situated
sufficiently near the symmetry center of the model to justify the ``centered
earth'' approximation. In the second work, we studied, in a peculiar subclass
of the DBB models, the extent to which the values of the dipole and quadrupole
moments measured in the cosmic microwave background radiation (CMBR)
temperature anisotropies can support a cosmological origin. This implies a
relation between the location of the observer in the universe and the model
parameter value: the farther the observer from the symmetry center, the closer
our current universe to a local homogeneous pattern. However, in this case, the
centered earth approximation is no longer valid and the results of the first
work do not apply. We show here that the horizon problem can be solved, in the
DBB model, also for an off-center observer, which improves the consistency of
this model regarding the assumption of a CMBR large scale anisotropy
cosmological origin.
