work for me in Unreal Engine 5.2.0
Thanks a lot! Worked for me in 4.27.2, 5.0.3 and 5.1.1!
Merhaba Ebru, Türk olduğun için seni buldum 
ben özel bir şirkette 3d modelleme uzmanıyım. Modelleme yapıyorum ama Unreal hakkında bilgi sahibi değilim bilgin varsa bir şery danışabilir miyim
you could just rename folder and press install so it pass check for empty folder and unlocks real install button
now you rename folder back
and then proceed with still unlocked install button (no cancelation needed)
btw should also work for games…
dunno why there is no checkbox to force install into existing folder
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It works, as of October 2023.
For anyone comes to this thread in the future, make sure you have waited for like at least 10 sec into the downloading (about 3-5GB downloaded) and EXITED the launcher NOT minimized to tray before folder rename/copying.
It didn’t work when i tried the first solution but your solution worked for me. Thanks a lot man! 
The fix for me (works November 2023):
- Rename original Unreal Engine folder i.e. “C:\Program Files\Epic Games\UE_4.25” to “C:\Program Files\Epic Games\UE_4.25(original)”…
- Begin the Unreal Engine install via the Epic Games Launcher, and then kill the launcher using Task Manager.
- Move the “.egstore” folder from the new install folder into the original folder that was renamed, then delete the new folder, then rename original Unreal Engine folder back.
- Restart the launcher and Resume the install. It might stall. If after 10 minutes nothing happens, kill the launcher and retry again (sometimes a “zombie” launch process stays loaded in memory - you need to kill it using Task Manager).
I had the same thing happen. I went to launch UE 4.25.4 recently and the launcher decided it was going to upgrade it to a later version automatically. I’m heavily vested into UE 4 already so I cancelled the update but then that broke the link between Unreal Engine and the Launcher. I could launch UE directly but not from the launcher.
It’s too bad Epic doesn’t have a simple “repair” option to fix this without having to jump through a bunch of hoops 
Thanks it worked for 5.4.2 but it failed for 5.3.2 maybe I did something wrong but in any case it saved me to download again one engine.
You are a lifesaver +10.000rep