That was "Beetle". Here is my writeup that I used for a presentation about Captured Eagles a few years ago.
P-47 Thunderbolt "Beetle"
On November 7, 1943, 110 B-17s from the 1st and third air division were assigned to bomb aviation industrial targets in Wesel and Duren. They were escorted by 283 Republic P-47 Thunderbolts, working in relays to provide cover for the bombers throughout the mission. Twelve P-47s from the 358th squadron of the 355th FG would fly their part, taking off with a spare aircraft in case any had difficulty. That spare, "Beetle", was flown by Lieutenant William E. Roach. Lieutenant John Lanphier developed engine problems and was unable to fly the mission. He returned to base while Roach formed up with Yellow Flight.
The mission was an uneventful mission until they reached the rendezvous point for their relief. The relief had been delayed due to weather. Colonel Cummings chose to stay and protect the bombers, a decision that would prove disastrous. Head winds caused them to burn more fuel than expected. Captain Walter Kossack, the yellow flight leader became disoriented and lost in the clouds. The flight became desperately low on fuel. Captain Kossack ran out of fuel and crash landed on the beach in Caen. Flight Officer Chester Watson ran out of fuel over the North Sea and bailed out to be captured by the Germans and made a POW. Lieutenant Jack Woertz was the only one from Yellow Flight to make it to England, where he crash landed at Hastings, just short of the runway. Lieutenant Roach watched his flight leader go down and looked around for options. He spotted a field nearby. Thinking he was in Southern England, he made a short approach and landed safely. He followed an airfield vehicle to a parking space and had shut down his engine when he realized that he was not in England! Germans approached with their guns drawn. They took him prisoner and he served the rest of the war in Stalag Luft I, with his flight leader, Walter Kossack.
Roach had landed at the Luftwaffe base in Caen. This was the first complete and flyable P-47 that the Luftwaffe had seen. American markings were quickly replaced with German markings. The Luftwaffe wisely chose to move the Thunderbolt inland to keep it away from allied strafing attacks. The P-47 was flown to Rechlin. There it was tested and evaluated thoroughly. The Germans gathered data on the performance, armament and handling of the P-47. During testing, the Germans found the Thunderbolt to be slow and difficult to fly below 15,000 feet. At higher altitudes, they were impressed with it's dive speed and roll rate. They were also impressed with the firepower of the 8 .50 caliber machine guns.
As with other fighters tested by the Luftwaffe, after a complete test and evaluation period, Beetle was released to "Zirkus Rosarius". Zirkus Rosarius was a special Luftwaffe unit under the command of Flugkapitan Ted Rosarius that visited front line fighter units to instruct Luftwaffe pilots on the characteristics, strengths and weaknesses of enemy aircraft. The Germans also captured and flew 2 other P-47 Thunderbolts.
Beetle also became a bit of a movie star. In early 1944, the German propaganda ministry used Beetle for a propaganda film. For the filming, the aircraft paint job was restored to it's original American markings. It was returned to Luftwaffe markings after the filming. Nazi propaganda films later also included a captured Spitfire for filming a propaganda film about the Battle of Britain.