Both MS Access and Filemaker support ODBC. So it is possible for either file to serve as the "back end" for the other. In otherwords one system can store the data and the other can read/write data from/to the same tables. It's not simple and you'll need to do some research if you've never done this before. There are a few threads in this forum on the subject. (Click the advanced search link above and try searching under terms like "ODBC" and "Access".)
These methods link the two database on a Local area network (LAN) not the internet, however.