  In [1] the authors showed some basic properties of a pre-order that arose in
combinatorial number theory, namely the finite embeddability between sets of
natural numbers, and they presented its generalization to ultrafilters, which
is related to the algebraical and topological structure of the Stone-\v{C}ech
compactification of the discrete space of natural numbers. In this present
paper we continue the study of these pre-orders. In particular, we prove that
there exist ultrafilters maximal for finite embeddability, and we show that the
set of such ultrafilters is the closure of the minimal bilateral ideal in the
semigroup $(\bN,\oplus)$, namely $\overline{K(\bN,\oplus)}$. As a consequence,
we easily derive many combinatorial properties of ultrafilters in
$\overline{K(\bN,\oplus)}$. We also give an alternative proof of our main
result based on nonstandard models of arithmetic.
