Moving SSH key authentication between client machines

I’m attempting to understand how to share my SSH access key between multiple client machines.
Desktop A
Desktop B
Server A

I setup ServerA from DesktopA via SSH public key authentication.
How do I add this same SSH key access to DesktopB so it can access same ServerA user?

can you sftp your keys from Desktop A .ssh directory to Desktop B .ssh directory?

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I’d use ssh-copy-id to add the public key:
(SSH password authentication should be on by default)

ssh-copy-id -i ~/.ssh/mykey user@host

For security i’d then SSH in using the key and turn off password authentication for SSH among other things.