Many printers only work with EITHER a USB connection OR a wireless one but NOT both. (I'm not sure whether that applies to all printers though).
However if the desktop PC is connected to a router (via an ethernet cable) all you'd need to do is to uninstall the printer driver, then reinstall it using the 'wireless' option. Then the desktop would talk to the router (via the ethernet cable) and the laptop would talk to the router (wirelessly), with both of them communicating successfully with the printer.