Provided the Sharp laptop meets the minimum requirements for Vista click here it may be slow but should work.
There used to be a checking tool but I think it has been removed.
You should also check the type of HDD in each laptop the Sharp may be IDE and the Fujitsu may be SATA this would make it near impossible to exchange HDDs.
You could, as a last resort, put the Fujisu drive into a caddy/dock and boot the Sharp from that if the specification are OK and you can select an external source to boot from. Failing these options I have no other suggestions.