This is the USA markings used for the foreign stuff tested by the Americans ... "FE" - Foreign Equipment or Foreign Evaluation.
AFAIK , the F1+DR code wasn't known when the Ar 234 was being restored. So the plane got the F1+GS markings of the 8./KG76 squadron that got the jet bombers as the first unit. Well .. it looks like there should be the "DR" instead of the "GS".
The plane could be operated by both the 7,8 and 9 Staffel ( III Gruppe ) because the transferring of planes among squadrons was something common, not during the war only but also at the war end. But it doesn't mean the markings had to be changed. A couple of sources states that the plane served both in 8 and 9 squadron of the KG76. It could be. Please, see the image of the F1+HT captured at the Sola airfield where the W.Nr.140312 was sent together with. The yellow colour of the letter "H" and the letter "T" indicate the 9./KG76. Because the plane code should be F1+DR so the squadron of the Ar 234 should be 7./KG76 though. The another thing the may make believing she also was of the 8./KG76 was that at the end of war all the planes in the Norway were gathered under the command of the Oblt. Kolm who was the 8th Staffel commander.
To sum up ... because there is too many cantradictions I would say the best way would be to use the III./KG76. Therefore I have edited my post with the form of unit marking. Unfortunately we criss-crossed our posts and you quoted the old content.
The marking is because of the Luftwaffe organization. The unit was Geschwader. Today, we call it a division. In the case we talk about the bomber division ( Kampfgeschwader). Each of the Bomber Division was marked with the Arabic numerals hence the KG 76 where the KG is the abbreviation for the KampfGeschwader.
The Kampfgeschader was divided into 3-5 regiments ( Gruppe ). Each Gruppe was marked with the Roman numerals eg ... I, II, III, IV, V.
The Gruppe was divided into 3 squadrons ( Staffel) usually. Each Staffel was marked with the Arabic numerals ( 1,2,3,4,5,6,7,8,9 ... etc ) although on planes it was a letter and also the colour used for the individual letter of a plane.
The first Gruppe (I) had the Staffel 1,2,3. The second Gruppe (II) - Staffel 4,5,6 and the third Gruppe (III) had the 7,8,9 for instance.
So .. to answer your questions ... what is the Gruppe , see above ... and would III./KG76 be correct, yes it is correct. Just it means the III Gruppe of the KG76.
About the F1+GS. The F1+HT is an example of the markings for the 9./KG76 that was sent to the Sola airfield together with the F1+GS. This may indicate the F1+GS could be operated by the 9th squadron too although the marking was of the 8./KG76.
Let me clarify again
Arado Ar 234B-2, Wk. No. 140312 served in III./KG76.
Transported to Sola Airfield in Norway, where it was captured by the British in May 1945 and then transferred to the United States by the Royal Air Force.
Renamed FE-1010, later T2-1010. ("FE" - foreign equipment)
All the paint was removed from it, apparently on purpose, then the Smithsonian Institution received it and began restoration and historically screwed up...
The fact is that Ar 234B-2, Wk. 140312 was originally numbered F1+DR, which is unknown when the Ar 234 was restored.
Therefore, the aircraft received the F1+GS markings of the 8th Squadron III/KG76, which was the first to receive jet bombers.
Most likely, the aircraft served in all 3 squadrons of the III regiment (group)
since the transfer of aircraft between squadrons was common not only during the war, but also at the end of the war.
Some say that the plane served in the 8th squadron, others - that in the 9th.
as the aircraft's historical tail number was F1+DR, it was automatically assigned to 7 Squadron III/KG76.
Another fact is that at the end of the war all Ar-234s are in Norway
were assembled under the command of Lieutenant Colma, who was the commander of the 3rd Regiment (Group) of the 8th Squadron. (Staffel)