Disconnect all users that connect to the db in Filemaker Mac OS, stop the db file. Copy the file and move it to a folder on filemaker server in Windows OS. Upload the file using the appropriate button. See page 22 of the document FileMaker Server 11 Help link manual: http://www.filemaker.com/support/product/docs/fms/fms11_help.pdf
Thanks! I will give this a try this coming Monday and will report back on how it works out. The FM Server interface is acting a bit wonky on the Mac side of things so I'm not sure if I'll be able to "stop" the database sharing but I will try my best.