1.) While printer on, open the printer lid to access the ink cartidges:

2.) Remove the problematic black ink cartridge:

3.) Inject ~10ml of home-made plum-brandy on black sieve filter using syringe:

4.) Insert black ink cartridge, close the printer lid, turn the printer off and wait for 3 days (meanwhile you can drink the rest of brandy
).
5.) After 3 days turn the printer on and try to print. It should print black even with non original black HP Ink Cartridge.