  We elaborate on the Green's functions that appeared in [1,2] when
generalizing, from massless to massive particles, various equivalences between
soft theorems and Ward identities of large gauge symmetries. We analyze these
Green's functions in considerable detail and show that they form a hierarchy of
functions which describe `boundary to bulk' propagators for large $U(1)$ gauge
parameters, supertranslations and sphere vector fields respectively. As a
consistency check we verify that the Green's functions associated to the large
diffeomorphisms map the Poincare group at null infinity to the Poincare group
at time-like infinity.
