Fax and time clock modem on the same phone line?

I have a client with two locations.     The main location has a computer that is used to poll time clock punches from a time clock at the remote location.    The system works with separate phone lines and modems at both locations.    The remote location also has a separate phone line for a fax machine.      

The client's question: Is there a device/splitter that would allow both the time clock and the fax machine to share one phone line?   My initial thought was no, because both devices (fax & time clock) are essentially modems.  

Any thoughts?