First, complete all the steps from the article FP4. Install Fairphone OS offline.

Apple macOS Monterey 12.2x Process

Once your Fairphone 4 is in Fastboot mode, connect it to your computer using a USB-C certified data cable.
Locate the archive you downloaded in the previous step, (usually in the Downloads folder).
Open Chrome Browser.
1. Press simultaneously the keys Alt ⌥ (option) + Cmd ⌘ + L. A new tab called Downloads will open.
2. Look for the last download, the name starts with FP3-.... Click on the writing Show in Finder.
  A new instance of Finder will open.
Open (Double-click) the archive you downloaded, the name starts with FP4.. The files will be extracted in a folder with the same name. Wait for it to be completed.
Once done, simultaneously press the Cmd ⌘ + Space keys. Spotlight Search will open.
Write Terminal.app, then press the Enter ↩ key.
In the Terminal window, type cd then press space.
Drag the folder extracted previously inside the terminal window, and press the Enter ↩ key.
Type ./flash_fp4_factory.command and press the Enter ↩ key.
If a similar error message appears:

Click on OK.
1. Go to the Apple menu (top left corner of the screen) →System preferences....
2. Click on the icon Security & Privacy.
3. Click on the General tab.
4. Click on Open Anyway.
5. Now, go back to your Terminal window.
Type ./flash_fp4_factory.command and press the Enter ↩ key.
The following warning will appear:
Type in Yes and Press the Enter ↩ key
The script will now run for a couple of minutes like in the following picture
Once done, you will see the following picture

-IMPORTANT-
It can take up to 15 min. Do NOT interrupt the process, it might damage the device!
Done, your phone is now up to date. Your phone will now reboot, finishing the system update for a few minutes. You can now safely unplug your FP4 from your computer.
Once done, for safety reasons, we strongly advise you to lock your bootloader again. To do so, follow the instructions in the article Manage the bootloader.