For any amalgam
(
S
,
T
;
U
)
(S,\,T;\,U)
of inverse semigroups, it is shown that the natural partial order on
S
∗
U
T
S{{\ast }_U}T
, the (inverse semigroup) free product of
S
S
and
T
T
amalgamating
U
U
, has a simple form on
S
∪
T
S \cup T
. In particular, it follows that the semilattice of
S
∗
U
T
S{{\ast }_U}T
is a bundled semilattice of the corresponding semilattice amalgam
(
E
(
S
)
,
E
(
T
)
;
E
(
U
)
)
(E(S),\,E(T);\,E(U))
; taken jointly with a result of Teruo Imaoka, this gives that the class of generalized inverse semigroups has the strong amalgamation property. Preserving finiteness is also considered.