How to add an installed game to steam (linux) ? [SOLVED]

[Mun]

Hello
I know the question has been asked many time but HEAR ME OUT ! I feel like I tried everything and nothing worked.
I installed a game purchased by a member of my steam familly on an external hard drive with another computer. I made sure to install it from my steam account and with a computer with the same OS. I want to transfer this game from my external hard drive to my computer and add it to Steam.
I tried putting it in the right folder (.../steamapps/common) and restart steam but it doesn't show anywhere on Steam. I tried fixing my library, didn't work. When I tried the "add a non-steam game" way, the game appeared as a .exe in my library, but when I click play it launchs but stops after 2 seconds (I tried many times, just in case). I found many guides about "add a steam library folder" stuff like that, but I think its outdated bc I don't have the same options in my settings. I also tried clicking on the .exe in the game folder but it just opens a sort of archive with text files in it.
I didn't find anything else on the internet, maybe I'm missing something. I have no other way to play this game because I don't have home internet, only my 4G (limited to 50 Go), and the game is 159 Go (what the ♥♥♥♥ btw) so I can't reinstall it (that's why I did all that). I'm a bit desperate tbh.
Anyway, Thanks for your help :)

[Kargor]

You need to copy the ACF file. They are in the steamapps folder; IIRC the numbers are the app-ids -- the same number that appears in the URL of the store page for the game.

[Mun]

Thank you SO much ! You are a life savior !!! It worked :))) I can't believe I missed something so simple in two hours of research.

PS :
For those (like me) who had no idea what it means : acf files are files called appmanifest_000000.acf, with the IIRC number (number that appears in the URL of the game's store page) instead of the zeroes. I found them in the SteamLibrary folder from my hard drive (created automatically when I downloaded the game). in the steamapps folder. I also copied to the corresponding folders the files named after the IIRC number in the compatdat and shadercache folders (idk if this is important but since they had the same numbers as my game I did it anyway).