We study germs of hypersurfaces
$$(Y,0)\subset (\mathbb {C}^{n+1},0)$$
(
Y
,
0
)
⊂
(
C
n
+
1
,
0
)
that can be described as the image of
$${\mathscr {A}}$$
A
-finite mappings
$$f:(X,S)\rightarrow (\mathbb {C}^{n+1},0)$$
f
:
(
X
,
S
)
→
(
C
n
+
1
,
0
)
defined on an icis (X, S) of dimension n. We extend the definition of the Jacobian module given by Fernández de Bobadilla, Nuño-Ballesteros and Peñafort-Sanchis when
$$X=\mathbb {C}^n$$
X
=
C
n
, which controls the image Milnor number
$$\mu _I(X,f)$$
μ
I
(
X
,
f
)
. We apply these results to prove the case
$$n=2$$
n
=
2
of the generalised Mond conjecture, which states that
$${\mu _I(X,f)\ge \text{codim}_{\mathscr {A}_e}(X,f)}$$
μ
I
(
X
,
f
)
≥
codim
A
e
(
X
,
f
)
, with equality if (Y, 0) is weighted homogeneous.
