All that needs to be done is the “id_rsa” key needs to be copied to the “new” host. You can do this with SCP or sftp.
Example with SCP
The following examples are showing how to export a RSA private key, if your using DSA, then replace id_rsa with id_dsa.
Copy private key from remote server to local machine for the local user
scp email@example.com:~/.ssh/id_rsa ~/.ssh/
Copy private key from localhost to remote host. This command copies the local users private key to the root user @ 192.168.1.1
scp ~/.ssh/id_rsa firstname.lastname@example.org:~/.ssh/