Me and two more friends bought the same game for Steam, can one of us (me in this case) download it and then send the files to my friends so they don't have to download it again?
I did this multiple time in college (1 year ago). Some of my friends had a really slow internet connection at home so I copied the game files on my portable HDD and transferred the files to them. They then copied it in the right folder and when clicking "install" in Steam, it discovered the files.
Doing this with games coming from a shared library also works, so you don't need to buy a game they have in order to download it for them.
You said in the question comments that you don't want to risk getting banned from this. There is no danger at all. You are not breaking any DRM while doing this. Your friends still need to buy the game if they want to use those files. If they don't own the game, it wont show up in their library.
Not for what you're looking to do.
Similar questions have solved how to move files between two systems under the same user account, and others solve how to migrate files on the same system for the same account, but you're asking how and if it's possible to migrate files between two systems and between two user accounts by downloading a copy on your system and then installing on to another from your download package.
Each system must download and install the files, there is no "customer courier" package do different users because of the DRM (some titles have third party DRM - so this can be an obstacle in some cases)
In the future, I'd suggest checking out the option to backup your games.
Steam does offer Family Library Sharing (FLS) which, depending on the game and how you and your friends play, could be of additional benefit.
Family Library Sharing allows selected accounts to use your game library on authorized computers while you're not playing. You can authorize up to 10 computers at the same time.
And, Steam stipulates the FLS option is not available for all games while providing a list of games within your specific library that are not available for FLS.