Amended Claims for National Phase Entry:

1. A downhole system for completing a well with wireless power and communication downhole, comprising:
- a first well tubular structure (1A),
- a second well tubular structure (IB) arranged partly inside the first well tubular structure,
- a first electrical unit (20) comprising a first inductive coupler part (20A) and being arranged on an outer face (21) of the first well tubular structure and electrically connected with an electrical conductor,
- an annular barrier (10) for being expanded in an annulus (2) between a first well tubular structure (1A) and a wall (5) of a borehole (6) or another well tubular structure downhole for providing zone isolation between a first zone (101) having a first pressure (P0 and a second zone (102), the annular barrier comprising:

- a tubular metal part (7) for mounting as part of the first well tubular structure, the tubular metal part having a first expansion opening (3), an axial extension (L) and an outer face (4),
- an expandable sleeve (8) surrounding the tubular metal part and having an inner face (9) facing the tubular metal part and an outer face
(16) facing the wall of the borehole,
- a first connection part (11) and a second connection part (12)
configured to connect a first end (13) and a second end (14),
respectively, of the expandable sleeve with the tubular metal part, and
- an annular space (15) between the inner face of the expandable sleeve
and the tubular metal part,
wherein the annular barrier further comprises the electrical conductor
(17) extending on the outside of the tubular metal part and within the
expandable sleeve from the first connection part to the second
connection part, and
- a second electrical unit (20B) comprising a second inductive coupler part (20B) and being arranged inside the first well tubular structure and arranged outside the second well tubular structure and configured to abut an inner face (22) of the well tubular structure, wherein the first electrical unit transfers power and/or communication to the second electrical unit.

2. A downhole system according to claim 1, wherein an outer face of the
second well tubular structure faces the wall of the borehole.
3. A downhole system according to claim 1 or 2, wherein the second electrical unit is electrically connected to a third electrical unit (20C) via a second electrical conductor (17, 17B).
4. A downhole system according to any of claims 1-3, further comprising a second annular barrier (10B) through which the second electrical conductor extends.
5. A downhole system according to claim 4, wherein the tubular metal part of the second annular barrier is a part of the second well tubular structure.
6. A downhole system according to any of claims 1-5, further comprising a lateral tubular structure (31) connected with one of the well tubular structures, and wherein a third electrical unit (20C) is arranged outside the lateral tubular structure.
7. A downhole system according to any of claims 1-6, further comprising a tool (50) arranged in the second well tubular structure, the tool comprising an inductive tool coupler part (51) configured to be electrically connected with the inductive coupler part.
8. A downhole system according to any of claims 1-7, further comprising a sensor (23) arranged outside one of the second well tubular structures.
9. A downhole system according to any of claims 1-8, wherein the annular barrier comprises a tunnel (18) arranged in the space between the first connection part and the second connection part, in which tunnel the electrical conductor extends.
10. A downhole system according to any one of claims 1-9, wherein the connecting parts of the annular barriers connecting the expandable sleeve to the tubular metal part are formed as tubular connection parts having a bore through which bore the electrical conductor runs.

11. A downhole system according to any of claims 1-10, wherein the first electrical unit and the second electrical unit communicate wirelessly through the first well tubular structure.
12. An annular barrier according to claim 1, further comprising a tunnel (18) arranged in the space between the first connection part and the second connection part, in which tunnel the electrical conductor extends.
13. An annular barrier according to claim 12, wherein the first connection part
and the second connection part have bores (26) through which the electrical
conductor extends.
14. An annular barrier according to claim 12 or 13, wherein the first connection part and the second connection part each have an electrical connection (24) configured to connect with the electrical conductor.
15. An annular barrier according to any of claims 12-14, wherein the connecting parts of the annular barriers connecting the expandable sleeve to the tubular metal part are formed as tubular connection parts having a bore through which bore the electrical conductor runs.