how to install a macOS installer package from an external HDD through recovery mode(without losing data)

Hey UnholyBerry,

We'd recommend reviewing this article as it provides your options for reinstalling macOS: How to reinstall macOS - Apple Support

"Reinstall macOS

Reinstalling macOS does not remove data from your Mac. To begin installation, select Reinstall macOS from the utilities window in macOS Recovery, then click Continue and follow the onscreen instructions. 

Follow these guidelines during installation:

• If the installer asks to unlock your disk, enter the password you use to log in to your Mac.
• If the installer doesn't see your disk, or it says that it can't install on your computer or volume, you might need to erase your disk first.
• If the installer offers you the choice between installing on Macintosh HD or Macintosh HD - Data, choose Macintosh HD.
• Allow installation to complete without putting your Mac to sleep or closing its lid. Your Mac might restart and show a progress bar several times, and the screen might be empty for minutes at a time.

After installation is complete, your Mac might restart to a setup assistant. If you're selling, trading in, or giving away your Mac, press Command-Q to quit the assistant without completing setup. Then click Shut Down. When the new owner starts up the Mac, they can use their own information to complete setup.

Other macOS installation options

When you install macOS from Recovery, you get the current version of the most recently installed macOS, with some exceptions:

1. On an Intel-based Mac, if you use Shift-Option-Command-R during startup, you might be offered the macOS that came with your Mac, or the closest version still available.
2. On an Intel-based Mac, if you use Option-Command-R during startup, you might be offered the latest macOS that is compatible with your Mac.
3. If you just erased your entire startup disk, you might be offered an earlier compatible version of macOS.
4. If the Mac logic board was just replaced, you might be offered the latest macOS that is compatible with your Mac.
5. You can also use these methods to install macOS, if the macOS is compatible with your Mac:
6. Use Software Update or the App Store 
7. Use a bootable installer

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Thanks!