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What maker and model # ***** printer do you have? I would dare to guess it's a Brother printer, but I'm not by any means sure at this point.
Some printers have a 'scan into memory' feature, to allow the rapid scanning in of a multi-page document that is going to be faxed out. If faxing out become impossible to actually do, this can fill the memory up.
Also, if received faxes cannot be printed out as they come in, they may be stored in memory instead.
So, either case can be relieved, if you make sure the device is indeed connected to a live phone line (so that faxing out can be done, from memory), and also make sure it is in a condition to print out pages, e.g. by checking ink levels, control panel display error messages (if any), and providing paper enough also. And doing one photocopied page successfully conclusively proves as a test, that the printer is in condition to print out.
After trying the above, if they fail to provide what you need, please provide to me the maker and model # ***** for the fax/printer, so that I can give a specific cure for the problem. Please quote, exactly and to the letter, the out of memory error message shown on the fax/printer itself. Thanks.