In the following link you'll see how to transfer an document from document tray to an file cabinet.
https://developer.docuware.com/dotNet_CodeExamples/290cce69-c600-400c-a4ca-89c305becf41.html
Technical the document tray is an file cabinet.
So you must change the direction of transfer to send a document from the file cabinet to a document tray.
But attention use the right document tray for the document with the same data structure.
You can see the relation under {your docuware server adress like yourcompanyname.docuware.cloud}/DocuWare/Platform/FileCabinets
where an document tray has AssignedCabinetId what is the Id of the connected file cabinet.
The inedx data will be preserved.