Hello Andrew,
As regards the spelling one can spell it Möbius (note the umlaut over the o) or Moebius if one doesn't have umlauts. Most German-origin sources I have seen use Leutnant der Reserve Martin Möbius.
As to whether Morey simply collided with Möbius or intentionally rammed him, who can say for certain? Since both unfortunate pilots died, we'll never know what was in Morey's head at the time. If one wants to believe that Morey intentionally rammed the German scout, no one can disprove this, I would guess.
Martin Möbius was born on 15 November 1984 in Annaberg. In April 1917 he was at Armee Flug Park 6 (AFP 6) as a pilot, and was assigned to Flieger Abteilung (A) 211 on 10 April; this was a two-seater reconnaissance unit specializing in artillery spotting. He was lightly wounded in action only 12 days later, on 22 April 1917 when he was shot down by two British aircraft identified as Sopwiths with his observer Ltn. Goldammer, at 0830 hrs. Möbius received a light wound in the right leg, but still managed to land his burning two-seater safely and the crew escaped further injury. He was awarded the Saxon Knight's Cross of the Military St. Henry Order on 22 June 1917, for this action. His somewhat erroneous (!) citation read:
"With conspicuous bravery Ltn. Möbius carried out numerous flights in the spring 1917 battles near Arras. He experienced many aerial combats before he was severely wounded (sic) on April 15 (sic) in an air battle behind enemy lines. With his last ounce of strength he brought his burning machine down behind his own lines."
On 9 November 1917 he received the Iron Cross First Class.
On 15 December he left the two-seater unit and went to AFP 4 at Ghent. He then went to Jastaschule 1 (at Valenciennes/Famars) and upon finishing the course for fighter pilots was assigned to Jasta 7 on 18 January 1918. Ironically, the unit's long-time CO., the ace
Josef Jacobs, was on leave since 2 January 1918. On 24 January Möbius had his collision with Morey and was killed; thus he never met Jacobs.
When he returned on 15 February 1918, Jacobs wrote in his diary that, "Ltn. Möbius, who was only a few days with the Staffel, collided with his opponent in his second victory." It would appear that, as was often the case, the Germans posthumously awarded Möbius with a "victory" for the SE5a that crashed in his fatal collision (it's all in your point of view). Despite Jacobs' statement that this was his second victory, there is no record anywhere of a "first" victory being attained by M in any unit.
The historian Stew Taylor wrote in his appendices to Jacobs' diary (as edited by Stephen Lawson and published in C & C Vol. 25 No. 4,1994 p. 90) that: "At 1210 hrs, 24 Jan. 1918 Capt. J.B. Crompton and Capt. F.O., Soden led a ten machine offensive patrol of 60 Sqdn SE5a's. Capt. Crompton returned with a loose high tension terminal and Capt. Soden continued to lead the control. About 1250 hrs an EA collided at 12,000 ft with Lt. A W Morey in SE5a B4897 over the German side of the lines. Both aircraft crashed southeast of Houthulst Forest."
The "SE5 File" and "The Sky their Battlefield" state that the collision took place southwest of Becelaere.
No source from either side says that the SE5a pilot deliberately rammed the German a/c, but who knows?