  Single-binary scattering may lead to an exchange where the single object
captures a component of the binary, forming a new binary. This has been well
studied in encounters between a star--planet pair and a single star. Here we
explore the application of the exchange mechanism to a planet--satellite pair
and another planet in the gravitational potential of a central star. As a case
study, we focus on encounters between a satellite-bearing object and Neptune.
We investigate whether Neptune can capture satellites from that object and if
the captured satellites have orbits analogous to the Neptunian moons Triton and
Nereid. Using $N$-body simulations, we study the capture probability at
different encounter distances. Post-capture, we use a simple analytical
argument to estimate how the captured orbits evolve under collisional and tidal
effects. We find that the average capture probability reaches $\sim$$10\%$ if
Neptune penetrates the donor planet's satellite system. Most moons grabbed by
Neptune acquire highly eccentric orbits. Post-capture, around half of those
captured, especially those on tight orbits, can be circularised, either by
tides only or by collisions+tides, turning into Triton-like objects. Captures
further out, on the other hand, stay on wide and eccentric orbits like that of
Nereid. Both moon types can be captured in the same encounter and they have
wide distributions in orbital inclination. Therefore, Triton naturally has a
$\sim$50\% chance of being retrograde. A similar process potentially applies to
an exoplanetary system, and our model predicts that exomoons can jump from one
planet to another during planetary scattering. Specifically, there should be
two distinct populations of captured moons: one on close-in circular orbits and
the other on far-out eccentric orbits. The two populations may have highly
inclined prograde or retrograde orbits.
