When trying to open the project for the first time, I always was asked to update the used project version (to 4.25.3).
After taking some time doing conversion stuff, then an error dialog opened with message:

ERROR: Building would modify the following engine files:
    /home/vvb/src/UnrealEngine/ue4/4.25/Engine/Intermediate/Build/Linux/B4D820EA/UE4Editor/Development/Engine/SharedPCH.Engine.h.d
    /home/vvb/src/UnrealEngine/ue4/4.25/Engine/Intermediate/Build/Linux/B4D820EA/UE4Editor/Development/Engine/SharedPCH.Engine.h.gch

Please rebuild from an IDE instead.

Even after build from my IDE (CLion), each time I tried to open the project again, Unreal Editor always crashed.

After searching forever a solution, I finally found this, stating to fix the FPSGameEditor.Target.cs: https://forums.unrealengine.com/development-discussion/c-gameplay-programming/1770131-solved-upgrade-c-project-from-ue-4-24-to-4-25-under-linux
This finally solved my issue and I was able to open the project again.