Problems sharing printer between 64 and 32 bit Win7 Ultimate

[skytex]

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 ?

 

[Parman]

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

 

[skytex]

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.

 

[Parman]

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/software12/COL22237/bi-101596-2/lj1020_1022-HB-pnp-win64-en.exe