Hello Scrimnet.
The MIC just says-
Rif Brig
Pte
S/10957
Ah well...Not many to chose from....
1st Battalion [1800-2001]
2nd Battalion [1805-1948]
3rd Battalion [1809-1819, 1855-1922]
4th Battalion [1857-1922]
Composite Rifle Battalion [1899-1900]
Militia and Special Reserve:
5th Battalion (The Queen's Own Regt of Tower Hamlets Militia) [1881-1953]
6th Battalion (The Prince of Wales's Royal Regiment of Longford Light Infantry) [1881-1899]
6th Battalion (Royal Longford and Westmeath Militia) [1899-1908]
6th Battalion (The King's Own Light Infantry Regt of Militia ) [1881-1953]
7th Battalion (The King's Own Light Infantry Regt of Militia ) [1881-1953]
8th Battalion (Leitrim Rifles Regiment of Militia) [1881-1889]
9th Battalion (Westmeath Rifles Regiment of Militia) [1881-1899]
Territorials and Volunteers:
[1st VB] 7th Middlesex (London Scottish) Rifle Volunteer Corps [1881-1908]
[2nd VB] 14th Middlesex (Inns of Court) Rifle Volunteer Corps [1881-1908]
[3rd VB] 15th Middlesex (The Customs and Docks) Rifle Volunteer Corps
[1881-1908]
[4th VB] 16th Middlesex (London Irish) Volunteer Rifle Corps [1881-1908]
[5th VB] 18th Middlesex Volunteer Rifle Corps [1881-1892]
[6th VB] 19th Middlesex (St. Giles's and St. George's, Bloomsbury) Rifle Volunteer Corps [1881-1908]
[7th VB] 20th Middlesex (Artists') Rifle Volunteer Corps [1881-1908]
[8th VB] 24th Middlesex Rifle Volunteer Corps [1881-1892]
[9th VB] 1st Tower Hamlets Rifle Volunteer Corps [1881-1892]
[10th VB] 2nd Tower Hamlets Rifle Volunteer Corps [1881-1892]
[4th VB] 18th Middlesex Volunteer Rifle Corps [1892-1908]
[7th VB] 24th Middlesex Volunteer Rifle Corps [1892-1908]
[8th VB] 1st Tower Hamlets Volunteer Rifle Corps [1892-1904]
[9th VB] 2nd Tower Hamlets Volunteer Rifle Corps [1892-1908]
5th City of London Regiment (London Rifle Brigade) [1916-1937]
8th (City of London) Battalion, The London Regiment (Post Office Rifles) [1916-1921]
10th London Regiment (Hackney) [1916-1929]
17th London Regiment (Tower Hamlets Rifles) [1916-1937]
25th (County of London) (Cyclist) Battalion, The London Regiment [1916-1920]
28th County of London Regiment (Artists Rifles) [1929-1937]
London Rifle Brigade [1937-1941, 1947-1960]
Tower Hamlets Rifles [1937-1941]
The Artists Rifles [1937-1939]
7th Battalion, The Rifle Brigade (PCO) (London Rifle Brigade) [1941-1947]
9th Battalion, The Rifle Brigade (PCO) (Tower Hamlets Rifles) [1941-1944]
The Rangers [1947-1960]
The City of London Yeomanry (Rough Riders) [1956-1961]
London Rifle Brigade/Rangers [1960-1966]
Hostilities-Only Units (First and Second World War, including T.A. duplicates):
2/5th (City of London) Battalion, The London Regiment [1916-1918]
5th (Reserve) (City of London) Battalion, The London Regt [1916-1919]
2nd Battalion, London Rifle Brigade [1939-1947]
2/8th (City of London) Battalion [1916-1918]
8th (Reserve) (City of London) Battalion [1916-1919]
2/10th (County of London) Battalion, The London Regiment [1916-1919]
10th (Reserve) (City of London) Battalion, The London Regt [1916-1919]
2/17th (County of London) Battalion [1916-1919]
17th (Reserve) (County of London) Battalion [1916-1916]
2nd Battalion, Tower Hamlets Rifles [1939-1947]
3rd Battalion, Tower Hamlets Rifles [1940-1941]
2/25th (Cyclist) Battalion, The London Regt [1916-1919]
25th (Reserve) (Cyclist) Battalion, The London Regt [1916-1916]
7th (Service) Battalion [1914-1918]
7th (Home Defence) Battalion [1939-1941]
8th (Service) Battalion [1914-1918]
9th (Service) Battalion [1914-1918]
10th (Service) Battalion [1914-1918]
11th (Service) Battalion [1914-1919]
11th (Home Defence) Battalion [1941-1942]
12th (Service) Battalion [1914-1919]
13th (Service) Battalion [1914-1919]
14th (Reserve) Battalion [1914-1916]
15th (Reserve) Battalion [1914-1916]
16th (St. Pancras) Battalion [1915-1919]
17th (Reserve) Battalion [1915-1916]
18th (London) Battalion [1915-1920]
19th (Western) Battalion [1915-1919]
20th (Northern) Battalion [1915-1919]
21st (Midland) Battalion [1915-1920]
22nd (Wessex and Welsh) Battalion [1915-1919]
23rd (North Western) Battalion [1915-1920]
24th (Home Counties) Battalion [1915-1920]
2/25th (County of London) (Cyclist) Battalion, The London Regiment [1916-1919]
3/25th (County of London) (Cyclist) Battalion, The London Regiment [1916-1916]
25th (Reserve) Garrison Battalion [1915-1916]
26th (Reserve) Garrison Battalion [1915-1916]
30th Battalion [1942-1943]
33rd (County of London) (Cyclist) Battalion, The London Regiment [1918-1919]
51st (Service) Battalion [1917-1920]
52nd (Service) Battalion [1917-1920]
53rd (Service) Battalion [1917-1920]
70th (Young Soldier) Battalion [1940-1943]
2nd Motor Training Battalion [1939-1944]
Have you thought of asking the museum at Winchester?