You would do the following
1) on the file server, move the current directory X contents to directory Y (temporarily). Directory X will now be an empty directory.
2) share a folder X on the windows box (can be the same name as the one on the Red Hat server, but doesn't have to be)
3) mount the folder X on the windows box to the Red Hat server (using either 'smbmount' or 'mount.cifs'; look at the man pages of these for more details). It is given a "mount point", which is your empty directory X on the Red Hat server. Once this is done, anything you place in directory X on the Red Hat server will actually end up on the Windows machine.
4) Copy the contents of temporary directory Y into directory X (effectively moving them across to the Windows machine). If this is successful, you can then delete directory Y.
Step 3 will only mount the folder until the next reboot. If you want it mounted permanently (ie, even after the file server reboots), you will need to place an entry in the '/etc/fstab' file.
Keep in mind this will be slower than serving directly from the Windows box, because you are transferring the files into the Red Hat server, and then back out to the Windows box (presumably over the same network link).
You should also be aware that the file systems on the two operating systems may behave a little differently, particularly when it comes to file permissions and time stamps.