As there is no reliable cross-platform file locking system, flag files are a common pattern for indicating process state. I worked with a system that had directories called "do", "done", "pending", "success", and "fail". The actual data file was dropped in the "pending" directory, then a file of the same name was created in the "do" directory. When the file transfer subsystem had done the transfer, it moved the "pending" file to "success", and moved the marker file from "do" to "done".
Can you get the sending process to create a marker file (either with an extension, a prefix, or in another directory) to indicate completion, and monitor for the marker instead?