We don't know who J Baker was, nor anything about his relationship to William. It's a bit tricky to work too much out about him from this address, but I take it to mean XI Corps Signal Cables Section. Signallers (Communications people) were needed at all levels in the army, and some would have been assigned directly to the Corps and served there. The fifth division - which William Whitmore belonged to - served with this Corps during the Battle of Hazebrouck during April 1918, and in the action at La Becque on 28th June 1918.
The table below lists all the engagements of the XI Corps. Please note: as with all tables like this one, remember that it lists only engagements with the enemy. Troops would spend considerable amounts of time each year in the trenches, and within firing range of the enemy. Shelling and sniping would be a permanent danger, which lessened (but did not disappear) when there was no major engagement.
| Campaign | Battle | Dates Present |
| Battle of Loos | Battle of Loos | 25 Sept. – 8 Oct. 1915 |
| Action of Hohenzollern Redoubt | 13 Oct. - 9 Oct. 1915 | |
| Battle of the Somme | Attack at Fromelles | 19 July 1916 |
| Posted to Italy | Late 1917 - Early 1918 | |
| German Offensive in Flanders | Battle of Estaires | 9-11 Apr 1918 |
| Battle of Hazebrouck | 12-15 Apr 1918 | |
| Battle of Bethune | 18 Apr 1918 | |
| Advance in Flanders | 18 Aug. - 6 Sept. 1918 | |
| Final advance in Artois | 2 Oct. - 11 Nov. 1918 |
Taken from The British Army in the Great War, and The Regimental Warpath.