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Try installing the same version engine on the directory to which you want to add your pre-existing engine under the name Epic Games.
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Wait for a min while it’s downloading. Pause it, and cancel the download.
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Name the downloaded Epic Games folder to Epic Games 123.
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Now, Select the pre-existing Epic Games folder in which you want to change its directory, and paste it into the folder next to Epic Games 123.
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Go back to Epic Games Launcher and click on resume. It will automatically start verifying your engine.
This is how you successfully change the engine’s directory.
Cheers.