Hello,
I found the solution on windows 7 for the Hp psc 1350 all in one.
When plugged the usb you must then go to
start>Devices and Printers
then
add printer (at the top of the page)
add a local printer
Use an existing port : USB001 (Virtual printer port for usb)
Click next
The hp psc 1300 series doesn't appear by default in the list so you have to push the button :
Windows update
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Now you have the hp psc 1300 series in the list. You must select it and follow the driver installation procedure.
Print a test page and voilà...
It has worked for me, hope it will be for you too.