Trouble printing from shared pc

I have my desktop with windows XP with sp3 hooked directly to an HP printer.
It works finer. I have a laptop with windows vista home premium and two user
accounts. The first user account can print perfectly thru the desktop and
shared printer. However, the second user account on the laptop cannot print
anything sent to the printer. The printer shows as available but doesn't
print when anything is sent from 2nd user account.

Any ideads on the issue and what needs to be done to fix this? Thanks.
Carl