Are non-finite amplimorphisms exhausted by infinite direct sums of finite ones?

Determine whether every non-finite localized and transportable amplimorphism in the category Amp of amplimorphisms of the allowed algebra B is isomorphic to an infinite direct sum of objects from the full subcategory Amp_f consisting of finite amplimorphisms (i.e., those with finite-dimensional endomorphism space (χ|χ)).

Background

The paper introduces the category Amp of localized and transportable amplimorphisms χ: B → M_n(B) of the allowed algebra B, and its full subcategory Amp_f consisting of those amplimorphisms for which the endomorphism space (χ|χ) is finite dimensional. This restriction to Amp_f is essential to establish equivalence with Rep_f D(G), since Rep_f D(G) contains only finite direct sums.

While Amp admits infinite direct sums, Rep_f D(G) does not. The authors therefore raise the structural question of whether all non-finite objects in Amp can be obtained as (possibly infinite) direct sums of finite objects from Amp_f. Resolving this would clarify how much larger Amp is than Amp_f and whether non-finite amplimorphisms introduce genuinely new sector-theoretic phenomena beyond countable sums of finite ones.