Force H was ordered to join the escort of Convoy WS 8B in the North Atlantic on 24 May, after the Battle of the Denmark Strait on 23 May, but they were directed to search for the and the heavy cruiser on 25 May. Heavy seas increased fuel consumption for all of the escorts and "Faulknor" was forced to return to Gibraltar to refuel later that day before rejoining the capital ships of Force H on 29 May, after "Bismarck" had been tracked down and sunk. In early June the destroyer participated in two more aircraft delivery missions to Malta (Operations Rocket and Tracer). On the 16th, after German blockade runners reached France, Force H sortied into the Atlantic on a unsuccessful search for more blockade runners. Together with "Fearless", , "Forester" and , "Faulknor" helped to sink on 18 June. Four days later, the 8th DF was tasked to intercept a German supply ship heading towards the French coast. The next day they spotted which was scuttled by her crew upon the approach of the British ships. They rescued 78 British POWs taken from ships sunk by German raiders as well as the crew. In late June, "Faulknor" screened "Ark Royal" and "Furious" as they flew off more fighters for Malta in Operation Railway.