openssl generate .key from CSR

JLMadruga asked:

A customer sent me a CSR and the .CER of a certificate for a linux server that I host. The customer does not have access to this machine.

Is this enough data to generate a valid certificate? Is it possible to generate the .KEY from the .CSR for a valid certificate?

My answer:

You can’t derive the private key from the certificate (signed public key) or the certificate signing request. If you could, the crypto would be utterly useless.

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