Problems sharing printer between 64 and 32 bit Win7 Ultimate

I have 3 systems each running Win7 Ultimate on a home network (not a home group). I have an HP Laserjet 1022 attached via USB to system #3 (32 bit). System #1 is 64 bit and #2 is 32 bit. System #2 prints fine on system #3. When system #1 (64 bit) prints, the entry is made into the print queue of #3, but never prints. I've tried restarting the print spooler to no avail. Print entry from #1 cannot be cancelled. I have to manually delete the spooler entry for the print job from C:/Windows/system32/spool/PRINTERS.
Without getting into finger pointing at HP, is there a problem with the printing software in Win7 when OS word sizes are mixed ? Is the HP Laserjet 1022 driver too old to be used (the driver states it was modified this current year) ? Is there a solution to this problem I've been having ?

Since both your 32 bit machines work and your 64 bit machine doesn't. Do you have the 64 bit drivers PC #1?

HP doesn't designate whether the driver they post for the HP 1022 is 32 or 64 bit. It has 2 drivers to download, but they both have exactly the same byte count, so it is likely they are identical.

You select your OS type before you actually see any drivers on HP site.

Here are the 64 bit drivers and an exe from HP ftp site.

http://ftp.hp.com/pub/softlib/softwa...p-win64-en.exe