A certificate comes in two parts. The certificate itself, which contains its public key, and a separate private key. When you install a certificate (or create one locally) you have both parts. Your recipient also has both parts of his certificate. What you need, to send a certificate encrypted document, is your certificate (including the private key), and his certificate, which contains his public key. You don't need his private key. How do you get his public key certificate? The easiest way is to send him a plain PDF with a digital signature field, and have him sign it with his certificate. When you receive the signed PDF, you can access the signature properties and export the public key certificate into your own key store. That's the piece you need to send a message to him. When he receives an encrypted PDF, he has your public key certificate (in the PDF you sent) and his certificate, including the private key. That allows him to open the file.
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