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

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

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