Move contents of a writable shared folder while someone possibly copying new files

Question

In simple: How can I move files from a shared folder without interrupting a just-copying network user in the windows environment?

Extended: We have two seperate network. Copying files from one network to other is done from only one point and it is done by IT people.

I want to automate the copying process as follows:

1. A pc(ServerA) in NetworkA provides a shared folder with subfolders with names of computers in NetworkB
2. A user(UserMachineB) from NetworkB use a pc in NetworkA and put his/her files to be transferred to \ServerA\Shared\UserMachineB
3. A script will be run on ServerA and put all the files from user folders to USB Stick. We can do Virus check, log transfers, etc. and put it to NetWorkB.

I want to move files from shared folder without annoying any user. Requirements are below:

1. xcopy only won't work cause I don't want re-copy, re-check those files. Somehow I should delete processed files/dirs.
2. net stop/start server may be useful but it may be annoying if someone is copying a big file and in the meantime connection got lost.
3. In my search I ran into a program syncback but I believe this would be solvable in windows shell and don't want to use 3rd party.
4. I don't have a req. to transfer files in one pack. So if someone is copying a big file or lots of files, it is OK to send some of them at later time but no files should have lost and directory structure should be preserved.