There is no one definitive answer to this question. It depends on the specific make and model of HP printer in question, as well as the type of generic ink cartridge being used. In some cases, it is possible to use generic ink cartridges in an HP printer without any problems. However, in other cases, using generic ink can damage the printer or cause printing errors. It is always best to check with the manufacturer of both the HP printer and the generic ink cartridge to see if they are compatible.