[22] He was appointed General Staff Officer 2nd grade from 1 June 1939 to 13 March 1942 with Rawalpindi District Headquarters in India.
[30] Greeves was advanced to Commander of the Order of the British Empire as temporary Brigadier, RIASC, for his service in Burma,[31] and also Mentioned in despatches three times.
[36] He was appointed a Companion of the Order of the Bath (Kings Birthday Honours) as Major-General, Special List, Ex-Indian Army.
This difficult task he planned and carried out most admirable and achieved his both his objects by hard fighting and tireless manoeuvre, during which he himself was always right forward, enthusing his troops and setting a wonderful example of fearlessness and dash, at all times completely regardless of his own safety, and quite indifferent to the fire of the enemy artillery, automatics and snipers to which he was subjected in each of the many actions fought by his Brigade.
Later, after a small bridgehead had been established across the Irrawaddy, he disengaged his Brigade with great skill and speed, and crossed over into the bridgehead; and thanks to fine planning, determination and speed, inflicted defeat after defeat on the Japanese, not only in close battle in the bridgehead area itself, but in a lightning sweep which carried his Brigade in four days over 35 miles of difficult country through the enemy’s artillery area, completely disorganizing it and various units of the 31st and 53rd Japanese Divisions to a position to threaten seriously the main Mandalay – Meiktila Road near Kyaukse.
His troops killed a great number of the enemy during this drive, destroyed many dumps of ammunition, petrol and supplies, and captured no less than eleven guns most of whose crews fought them to the last.
He has throughout shown all the qualities of a great and fearless leader, and has carried out with his Brigade in one month the many difficult tasks given to him in such a brilliant way that he is most thoroughly deserving of the immediate award of a Bar to the Distinguished Service Order.