If you want to allow another user to login to a server with the same key as another user (which is terrible!), you should login as the user with the key you want to copy and run the below rsync command, replacing username with the username of the user you are copying the key too.

rsync --archive --chown=username:username ~/.ssh /home/username

Then afterwards try logging in to the server as that user, and you should be able to.