I am using the action Run playbook in Phantom. Splunk can send the alert, but without fields created on Splunk. I have created the same fields on Phantom but the mapping was not performed.
Using the Phantom App for Splunk would be recommended for performing field mappings in that way:
You can utilize either a Saved Search or Data Model to have events from Splunk Core/ES which meet the defined criteria in your SPL forwarded to the Phantom instance of your choice: