Have you tried printing locally?
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Using HPlips, I got it to work on one laptop. It requires the use of a GUi and very temperamental for some reason. I can only give print commands from the HP printing center software where I need to click and drag files into it to get it to print.
It is very inconvenient.
This person blogged about it and offers two ways of making it work https://www.dongdongbh.tech/setup-hp-1020-priter-on-linux The second method doesn't need a GUI it seems, and for the first method you could use VNC, or ssh -X, to have the pi's desktop on your computer for the hplip GUI.
The openprinting page has another thing to say about it : https://openprinting.org/printer/HP/HP-LaserJet_1020
The firmware of the printer must be uploaded after turning it on. You can use a hotplug/udev script which comes with foo2zjs, or do it manually: "cat /usr/share/foo2zjs/firmware/sihp1020.dl > /dev/usb/lp0".
I had one of these about 10 years ago. The Linux device manager will be able to push the firmware file automatically provided it’s in the right directory on the filesystem. Check /var/log/syslog and dmesg when you power up or plug the printer in. The firmware should go in /lib/firmware/hp, file name sihp1020.dl.