Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
Your Brother printer has presumably, if it is not receiving faxes and is saying 'Full' or 'Memory Full', been receiving into memory without printing out any fax.
So what you need to do is
1. restore the printing capabiliy - make sure the printer *can* actually print out received faxes, in case that is a problem. Make sure of paper supplied in tray(s), that ink/toner is not a problem, etc.
2. print out faxes from memory. Each one printed out will make room for more to be received.
3. also, you could change the Brother printer's fax settings, so that it does not receive into memory, but instead prints out whatever it receives.
Let me know if you need further details on any of this, and also let me know if I have made a wrong assumption about any detail.