They could use the building's electrical supply cabling to make a network so computer 'B' can connect to computer 'A' and share its internet connection. That way both computers can access the net at the same time.
They'd need to buy a powerline network device for each PC. The gizmo takes the PC's network traffic & superimposes it over the standard electrical wiring in the building to be received by the other PC's gizmo.
They're available in the UK & US but not sure of the price.