I did it... I achieved my goal... I can now contol my air conditioner from Home Assistant!
I'm so happy and proud of myself!

All went so fast in just a week I still can't believe it. Here is a brief summary of what I did and how:

   1. Using this GUI tool, I created a firmware with the following settings:

• Board type = CC2530
• Device type = End device without routing
• Status LED = P22, Sending reports
• Output 1 = P03, UART, Baud rate = 9600, Packet end = 0x0D
• Model ID = RAS-LJ22Y_ADPT (setting of an unique name)
• Set default reporting interval(s) = 60
• Update firmware's timestamp

   2. Before closing the GUI tool, I used "Save custom converter for Z2M" to create the corresponding external converter for Zigbee2MQTT (see file A-C_Hitachi_converter.js).

   3. I flashed my Zigbee module, powered it up and then moved to Zigbee2MQTT dashboard in HA in order to add it. It appeared as an unsupported device with the name "RAS-LJ22Y_ADPT" so I followed the indication on this page and added it without any problem. 

   4. Then I moved the external converter I previously created to /config/zigbee2mqtt/.

   5. Back to Zigbee2MQTT dashboard, I went to Settings > External converters, entered the name of the converter, clicked "Submit" and restarted Zigbee2MQTT. The result is as follow.

   6. I added a climate platform to my configuration.yaml following this documentation (see file climate_platform.yaml for more details.) and restarted HA.

   7. In the meantime, I wrote a simple program that retrieves the air conditioner status every 2 seconds, compares it to a previous known status and if different, sends it to HA in a JSON format. Also, this program send setting commands to the air conditioner according to what have been received from HA (see file my_puny_program.ino for details).

   8. Finally I added a "Thermostat card" in Lovelace and set the "Entity" to the climate entity I created.

I played a lot with this "Thermostat card", also played a lot with the infrared remote control and so far everything works perfectly, everything is in perfect sync. Only problem is how the material solution looks like for the moment...