Ah. Missed this one earlier.

Fault in the printer, then, or a fault in the connection between the printer and the ink cartridge. Once upon a time, HP printers used to include the inkjet nozzles along with the cartridges. Epson was the one brand, IIRC, that kept the inkjet nozzles on the printer itself and they always clogged, chronically. But HP used to always be OK if you replaced the cartridge. So unless they've changed the design, I'd say the printer is faulty rather than the cartridge or the ink nozzle.

Do Bitt's printer-self-test to be sure first, then recommend the client get a color laser.