In order to change the owner of an SSH connection, click on the checkbox to left of the SSH connection name and click Change Owner. Upon clicking Change Owner link, a popup will appear that shows all of the users to whom you can assign the selected SSH connection to. Once you select a user from the drop-down presented and confirm, that user will become the new owner of the SSH connection. Only owner of the SSH connection can perform this operation.
You can alternatively click on the SSH Connection name to get to the SSH Connection edit screen and then select a user from the Owner drop-down presented below and hit Save.
