Source: Michael Doyle Their Name Liveth For Evermore: The Great War Roll of Honour for Leicestershire and Rutland.
He was the son of Joseph Adams, a hosiery trade hand frame knitter, born 1868 in Leicester and his wife Mary Craxford Adams (nee Pridmore, married in the 3rd quarter of 1888 in the Billesdon, Leicestershire district), a boot and shoe trade machinist, born 1869 in Leicester. Archibald was born in the 3rd quarter of 1895 in Leicester, his siblings were, Alfred, born 1889, Annie, born 1891, Ada, born 1894, Sarah Gertrude, born 1898 and William Joseph, born 1900, all his siblings were born in Leicester, in March 1901 the family home was at 9, Stone Bridge Street, Leicester. In April 1911 Archibald was employed as a hosiery apprentice and was residing in the family home at White Street, Kibworth Beauchamp, Leicestershire together with his father a hosiery trade framework knitter, his mother and siblings, Alfred, a hosiery framework knitter, Annie a hosiery trade binder, Ada, a hosiery trade binder, Sarah, a hosiery trade runner on, William, a schoolboy, Mary Elizabeth, a schoolgirl, born 1904, Florence, a schoolgirl, born 1907 and George, born 1909, the latter three siblings were all born in Kibworth Beauchamp. Archibald died of his wounds in the 28th Casualty Clearing Station, France, he was awarded the British War and Victory medals.
On Friday December 15th 1916 The Melton Mowbray Times & Vale of Belvoir Gazette published the following article under the heading. “KIBWORTH.” – MEMORIAL SERVICE. – At the Parish Church on Sunday morning, a memorial service was held in memory of Lance-Corpl. Archie Adams (who died in France last week from gunshot wounds). The rector eulogised the deceased as an old chorister and scout boy. The Kibworth troop of Boy Scouts sounded the “Last Post,” and the organist played the Dead March.

Source: Leicestershire War Memorials Project.
This is probably the same A Adams who was commemorated on the Bridge Street School Memorial, as Archibald Adams grew up nearby, on Stone Bridge Street, Leicester