trying to decrypt the ask here.... sounds like u want to print all faxes received by the pbx... easiest solution that is free off the top of my head is just send all the faxes to a mailbox and in the spirit of being free we can send them all to a gmail account, use the open source mail client thunderbird create a rule to print all the emails to a specific printer.
Also most printer today let you setup an email account to connect your printer to the cloud and it is usually setup so you can just email that account and it prints whatever you toss at it....
I would also look into google cloud print... with a gmail account you may be able to remove thunderbird from the original idea I had.. Although I am curious if there are an other ways....
I have one CX that requests this and I just use an O365 account for this, but this doesn't meet the financial requirement here.