OK, Arthur William is in my files. I've been having eye problems to there may well be typos, but here is the information I have gathered. The available information started drying up after 1902, so I have supplemented the information from the surviving Reformatory records with census data and newspaper reports. Hope it is of interest.
No. 1505
Name: Arthur William Hall
Address: 2 Pelham Street, Lincoln [1901 census]; 34 Michaelgate, Lincoln [1908 newspaper report]
Whence received into Saltley: Lincoln Police Court
Offence: Stealing 9s 6d [newspaper report]
Date of Admission: 10 September 1908
Parents: Arthur K and Elizabeth Hall [1901 census]
Parents occupations: father - Crane worker[?] in oil mill; mother - none [1901 census]
Additional:
12 September 1908 The crime that sent him to Saltley was reported in the Boston Guardian Saturday 12 September 1908 p.2 col.2: THEFT BY A LINCOLN NEWSBOY. Lincoln City Police-court, on Tuesday before Mr. T. Martin and Mr. J. S. Battle, Arthur Wm. Hall, 12, St. Michael-gate was, charged with stealing 9s. 6d. .from Wm. Baker, of 26, Canwick-road, on September 5th. - Detective-sergt. Brierley and prosecutor gave evidence. It appeared that the boy had delivered newspapers at the house of prosecutor. On Saturday night prosecutor gave him what he believed at the time was 6d. Subsequently he discovered that he had given him half-a-sovereign, The boy, who gave him 3d. change, retained the half-sovereign, and on being questioned bv Detective-Sergt. Brierley admitted that he had kept it, and that he had given some money to other boys, and had bought sweets and gone to the Palace Theatre. The accused now explained that he did not know that he was paid half-a-sovereign till afterwards. as he had put the money straight Into his pocket, and when he discovered it another boy urged him to spend it. - The father of the accused said that prosecutor was guilty of negligence in giving the half-sovereign to the boy. - It was stated that the accused had been before the magistrates twice. - The magistrates now sentenced him to receive six strokes with the birch rod, and to be sent to a reformatory.
8 July 1909 The following year his father was in trouble, as reported in the Lincolnshire Echo Thursday 8 July 1909 p.3 col.3: FAILING TO MAINTAIN. - Arthur Hall, of 34 Michaelgate, Lincoln,.was summoned for failing to pay 1s a week maintenance for his boy, Arthur Wm. Hall, who was sent to the Saltley, Warwick, reformatory school in September last. - The Chief Constable stated that since the boy was sent away the defendant had only paid 8s. Defendant, on the committal of the boy. had volunteered a shilling a week The man had been in good work for some time. - The Mayor said this was a case of utter neglect An order of 1s a week was made.
25 July 1913 The Reformatory Incidental Returns Register recorded that Hall was licensed to go out and work for Mr Astley Bates, builder, Small Heath, Birmingham
7 September 1913 Sentence expired whilst out on licence, discharged from Saltley