Could the younger officer be David Cuthbert Thomas ? Sassoon, Graves and Thomas were close friends - Graves said they "always knocked around together".
At the Regimental depot, Sassoon and Thomas shared a room - Thomas, though about 9 years his junior, acted as Sassoon's mentor in all things military, because he had just graduated from Sandhurst. In 1916, at Bois Francais near Fricourt, Graves was in "A" Company of the 1st Battalion RWF; Sassoon and Thomas were both in "C" Company .
Graves, at various places, describes David Thomas as having great charm and being below average height; conventionally good looking; fair-haired.
Thomas was killed on 18th March 1916. ( Graves and Sassoon attended his burial; Graves describes how Sassoon completely broke down, so he hurriedly got him away before anyone noticed.)
Sassoon is not wearing his MC ribbon in the photograph. That was gazetted on 27th July 1916 - though Sassoon says he was told of the award just before he entered the assault trench, at Fricourt, on 1st July 1916.
If the 1916 photograph really does show David Thomas, it must - obviously - have been taken before 18th March. At that time, Sassoon would not have worn the MC ribbon.
Tantalisingly, you have another photograph, titled Siegfried Sassoon with officers. It is dated May 1916. Does that carry any names ? Does the same young officer appear in it ? If so, it cannot be David Thomas in the first photograph.
Clive Rainbow. "