While a Hewlett Packard (HP) inkjet cartridge can be refilled easily, getting it to work again in the printer is another matter. The contacts on the back of the cartridge are programmed to read the ink level, but they don't reset for the printer just because you add more ink. You must get the printer to recognise the cartridge as new. You can do this easily if you have two other old cartridges, or you can manipulate the contacts on the refilled cartridge.
Insert the cartridge you refilled into the HP printer. Have the printer print an alignment page, thus recognising the cartridge. The printer will still read the ink level as where it was before you refilled it.
Remove the cartridge from the printer and replace it with another old cartridge. Have the printer print an alignment page with this cartridge so it recognises it as a different cartridge from the first one.
Replace the second cartridge with a third one and run the same alignment page. Because the printer only retains the memory of two print cartridges, it will erase the memory of the first (refilled) cartridge.
Insert the refilled cartridge into the printer. The printer will now recognise the cartridge as being full.
Tape over the contact squares on the top left corner of the cartridge's contacts. Insert the cartridge into the printer and run an alignment page. Ignore any messages that might appear saying there is a problem with the cartridge.
Take the cartridge out of the printer. Remove the tape from the left corner and tape over the contact squares on the top right corner. Place the cartridge back in and run another alignment page.
Remove and reinsert the cartridge, this time with no tape on any of the contacts. Check to see if the printer recognises the cartridge as being full.
Repeat the above steps if the cartridge is still shown as being empty. This time, use the bottom corner contact squares instead of the top ones. If you are still unable to reset the cartridges, using multiple cartridges is likely the only way to do it.
If you have three cartridges, refill all three of them and label them as "1", "2" and "3". By cycling them in sequence, you can keep resetting the cartridges and using all three repeatedly.