Faulty GBA SP question?

Hello so i sold someone a gba sp, limited mario one and they have messaged me stating that its faulty and wont save games, and they have tested cartridges on this Gba and another but surely game saves are only to do with the cartridge and not the console?

I told him I would get some expert opinion though im fairly sure the console itself has no memory to save or anything like that and it would be down to a dodgy cartridge? He has probably just changed his mind anyway so if I prove him right im sure the console will suddenly develop another fault and ill have to refund. LOL

Thanks in advance. Keith