After many hours reading different versions of manuals I found out, that's not possible to perform a pairing operation between Icon HD Tank Module and the computer without pressure on a tank.

The hint that's the manual is wrong is inside the Erate Corrige:

In Section 1.8 it is mentioned that the tank module does not need to be mounted on a regulator first stage. This is incorrect. To perform the pairing operation, the tank module must be pressurized to at least 15bar/220psi. Hence it must be mounted on a first stage regulator, which is itself mounted on a full scuba tank and the valve opened.

Hopefully the battery of the Tank Module is full and I'm able to pair both devices tomorrow at Helengeli Island.

Key Features of ICON HD:

• Max depth 150m
• Digital compass
• Decompression model: RGBM Mares - Wienke (10 tissues)
• Extended display
• Wide screen for superior readability
• Digital descent/ascent speed indicator
• Air integrated (Tank pressure, breathing rate)
• Nitrox with option to use up to 3 different mixes
• Bottom Time/Gauge with stopwatch
• Seabed map available during dive
• USB interface to PC
• Temperature measurement
• Logbook for 100 dives

It's my first dive computer and I think it's currently one of the best dive computers for divers who wants to enjoy a secure dive.