|By the way|
- 1284-A is the 25 pin D-sub connector.
- these USB to parallel printer adapters are meant to be connected to printers, NOT to multi-function devices (all-in-ones - printer/scanner, etc.) or other devices with a parallel port (e.g. older scanners). The printer functions of your all-in-one may work fine, or they may NOT, but the other functions of the all-in-one likely WILL NOT WORK because the circuits for the adapter likely don't support other than use with printers.
If you want all of the functions of the all-in-one or another device other than a printer to work for sure, you need to connect to a standard enhanced parallel port (capable of and set to EPP, ECP, or EPP/ECP mode).
E.g. if you have a desktop computer, if it has a parallel port connect the device to that. If you don't have a parallel port available, get yourself a PCI parallel port card and connect the all-in-one or other device to that.
(There is no speed advantage to connecting via USB - a USB connected parallel printer can't run any faster than it does max when connected to a parallel port.)
Why didn't you mention you already had tried a typical USB to parallel printer adapter in the first post?
It was NOT obvious in the document you linked to above that the centronics connector on the printer is smaller.
I tool another look.
In the support for the PSC 500 all-in-one's (it's incorrect to call it a printer) I found:
"The connector is smaller and allows smaller printed circuit board designs (thereby allowing smaller printer designs)"
"The downside to selecting this cable type was that it is not readily available in the retail supply chain at this time.
Other names for cables of this type include:
IEEE 1284 A-C"
That's typical of HP to sometimes use something that isn't widely supported.
Apparent there are two types of 1284-C.
The Centronics connector on your all-in-one is Centronics MICRO - the normal used one is called Centronics MINI, or just Centronics.
They're both 36 "pin", and they look identical except for their size.
HP doesn't have any pictures that I could find of the parallel cables for them but apparently it must have the connectors the same as on this one:
Computer Cable, 6-ft. IEEE 1284 AC Parallel Cable DB25M to MicroCen36M
SO - what you do is search for:
USB to centronics micro adapter
USB to centronics micro printer adapter
or - if you already have a typical standard USB to printer adapter (to centronics or centronics MINI).....
centronics mini to centronics micro adapter
centronics mini to micro adapter
USB Micro Centronics Conversion Kit
USB to micro centronics
(circuits within the adapter; cable used is USB)
Cable - USB to Micro Centronics printer adapter, but out of stock:
Regular USB to printer (Mini C) adapter
Optional Mini-C/Micro C Adapter Available
"This 6-foot USB to Parallel IEEE 1284 Centronics 36 adapter allows you to connect your parallel printer to a USB port on your computer. The parallel end fits directly into the centronics connecter on your printer (36-pin).
This adapter WILL NOT WORK with your all-in-one printer."
Just the adapter:
Incorrect labelling - should be to Micro - looks like the same thing