In order to change the owner of a SOAP connection, click on the checkbox to left of the SOAP 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 SOAP connection to. Once you select a user from the drop-down presented and confirm, that user will become the new owner of the SOAP connection. Only owner of the SOAP connection and a user with admin role can perform this operation.

You can alternatively click on the SOAP Connection name to get to the SOAP connection edit screen and then select a user from the Owner drop-down presented below and hit Save.