I found an answer in the NCryptTranslateHandle function documentation:
This is a helper function intended to help
applications and system components that currently use the CryptoAPI to
make a graceful transition to using CNG.
This function will only be successful if a CNG key storage provider is
registered with a name or alias that is identical to the name of the
cryptographic service provider (CSP) referred to by the hLegacyProv
parameter.
This function will perform the following steps to translate the CSP
handle into a CNG key handle:
Obtain the name of the CSP from the hLegacyProv handle. Open the CNG
provider whose name or alias is identical to the CSP name. Obtain the
name of the current key container in the CSP. Obtain the CryptoAPI
key, translate it into a CNG key, and return it in the phKey
parameter.
Registering the KSP with the same name or alias as the CSP does the trick.