Sounds like you have download macOS Sierra, this downloads as InstallOS.dmg
which you then open to get InstallOS.pkg.
You then open that and get an installation window, this will say it takes 7MBs of disk space,
No Operating System only takes up 7MBs of space. This is not installing macOS Sierra but
creating the Install macOS Sierra.app which you will find in your Applications folder.
You use the installer app to install mac OS Sierra on the other mac.
If you have downloaded El Capitan it works in the same way.
You started out asking about macOS High Sierra as that is what the mac had been running previously.
It is still available, why did you not download that.
Open Safari and click on this link,
How to get old versions of macOS – Apple Support
Go to the Download OS section and click on macOS High Sierra this redirects you
to the App Store High Sierra page it should say Get or Download.
This will download the full installer app for macOS High Sierra to your Downloads folder.
It is 5.23GBS in size and is all you need to install a full working version of macOS High Sierra 10.13.6.
No need for Combos or version 10.13, it no longer exists.
Connect your mac to your router via cable rather than rely on WiFi.
Do not use your mac while it is downloading
and do not use any other devices that share the same internet connection.
If the App Store says ‘Open’ then it is detecting a previous download of the install app
go to the Applications folder locate Install macOS High Sierra.app.
Move it to the Trash, empty the Trash.
Restart, click on the link again, the App Store should say ‘Get' or 'Download'.
To install any of these installer apps on your friends mac you need to create a bootable USB flash drive.
16GBs or larger. Rename the USB flash drive as MyVolume.
Please note there is a problem with doing this for Sierra which there is a workaround for but I won't tell you
as you really want macOS High Sierra.
How to create a bootable installer for macOS – Apple Support
With Install macOS High Sierra.app in your Applications folder open the Terminal app from Applications> Utilities.
copy and paste this command
sudo /Applications/Install\ macOS\ High\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume
press Return
enter your password (any input will not be echoed on screen)
press Return
follow the prompts
after initial activity Terminal will look like it is not doing anything, it is
be patient the process takes about 20-30 minutes.
It has completed when you see the
<username>$
prompt.
The bootable USB should be plugged directly to your mac.
Restart the mac while pressing and holding the option/ alt key.
In a minute or two you will see the Startup Manager, select the USB and press Return.
When booted to the USB you will see a Utilities panel, select Disk Utility and press Return.
Click View in the menubar and select Show All Devices.(This instruction is for macOS High Sierra and newer)
In the left hand panel highlight the Disk (Apple SSD… or similar) not any indented Volumes.
Click Erase.
Give the Disk a name.
Format: APFS for macOS High Sierra, Mac OS Extended (Journaled) for El Capitan or Sierra
Scheme: GUID Partition Map
Click Erase.
When Done Quit Disk Utility.
Click on Install OS press Continue the installation process should start up
follow the prompts.
