I take it you are on a dial-up internet access account.
What you want to do will not work unless you have 2 phone lines (or broadband). While you are online, the modem you are using to access the internet is using the phoneline and therefore the fax will not be able to send or receive while the phoneline is in use (i.e., you are online).
Similarly, you cannot make (or take) a phone call while you are online as the modem is using the phoneline to send and receive data while you are connected to the internet.
Hope this helps