Save as PDF to Sorter

Apologies if this is very basic, but I haven’t been able to find an answer elsewhere . . . is there a way to create a script for the “PDF” print button analogous to “Save PDF to DEVONthink Pro.scpt” but that sends the PDF to the Sorter without the need to open Devonthink itself? I know you can save the PDF first and then drag it onto the Sorter, but is it possible to make it direct?

Which database/group in Sorter would PDF documents be saved to?

Would saving to the Inbox folder (~/Library/Application Support/DEVONthink Pro 2/Inbox) associated with the global Inbox be an alternative?