For the move, you need to export the certificate as well as the private key from your previous server. This will allow you to reinstall the SSL certificate on your new server.
For transferring the certificate from one IIS to another IIS, you can use our instructions.
Unfortunately, without the associated Private Key, there is no way to transfer an SSL certificate from one server to a new server. If you do not have the PrivateKey anymore, you can simply reissue it for free via your customer account. First generate a new CSR on your web server or via our CSR generator. Then log into your account, go to the certificate details and click on the "Modify" button. In the window that appears, you have the option to add the new CSR and initialize the reissue. After successful validation, the certificate will be reissued.