If the goal is to retrieve the file from Server A, process it on Server B and then move them to Server C...
Use ListSFTP to retrieve the file list from Server A
Use FetchSFTP to retrieve the file from Server A and copy it into a flowfile on Server B. In the processor Properties, set Property Completion Strategy to "Delete File". That will remove the file from Server A after it is successfully turned into a flowfile.
Use PutSFTP to copy the flowfiles out to a file on Server C
I think that accomplishes what you want and the file is still in NiFi on Server B for whatever additional processing is needed.