  We introduce the formalism to describe heavy-ion Double-Charge-Exchange (DCE)
processes in the eikonal approximation. We focus on the low-momentum-transfer
limit -- corresponding to the differential cross section at $\theta=0^\circ$ --
and, for the first time, we show that it is possible to factorize the DCE
cross-section in terms of reaction and nuclear parts. Whereas in the
$\theta\neq0^\circ$ case the nuclear part is a convolution of the beam and
target nuclear matrix elements (NMEs), for $\theta=0^\circ$ we demonstrate -
for the first time- that the transition matrix elements can be written as the
sum of Double-Gamow-Teller (DGT) and Double Fermi (DF) type parts, and that
they can both be further factorized in terms of target and projectile NMEs. By
making use of the Interacting Boson Model (IBM) formalism, we also show that
the DGT and total parts of the neutrinoless double-beta decay NMEs are in
linear correlation with DCE-DGT NMEs. This confirms the hypothesis of a linear
correlation between them, as introduced in [Phys.\ Rev.\ Lett.\ {\bf 120},
142502 (2018)]. The possibility of a Two-Step Factorization (TSF) of the very
forward differential DCE-cross-section and the emergence of DGT and DF types
for the DCE nuclear matrix elements, combined with a linear correlation between
DCE-DGT and 0$\nu\beta\beta$ NMEs, opens the possibility of placing an upper
limit on neutrinoless double-beta decay NMEs in terms of the DCE experimental
data at $\theta=0^\circ$.
