Running the Exchange Hybrid Configuration Wizard (HCW) on Windows Server Core is not supported.
The Exchange Hybrid Configuration Wizard requires a graphical user interface (GUI) to run. To run HCW, you'll need to use a version of Windows Server with a Desktop Experience (the full GUI) or run it from a client machine like Windows 10 or Windows 11.
Alternatively, you can run the HCW on a management workstation or another server with the Desktop Experience, and it will still configure the hybrid setup for your Exchange environment.
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hth
Marcin