I assume that you have his service record from FindMyPast.
The entries below the Field General Court Martial sentence dated 28 January 1901 indicate that he was released from Derby Prison on 26 September 1901 on the authority of the Adjutant General's letter reference 110/37/199 from the department AG4 (which I assume dealt with disciplinary matters). He then continued to serve until he was finally discharged on 12 Jun 1912 having completed 16 years service and was due for a pension based on 6 years and 160 days service.
It therefore looks as if his sentence was not confirmed, or that perhaps he successfully appealed against his conviction. The National Archives do not appear to hold any documents relating to his case, which is surprising, but only a percentage of the documents relating to Courts Martial were retained. For example
registers of Courts Martial held in South Africa from April 1901 exist, but I can't find the records for earlier trials.
There is an extremely small chance that a copy of the letter authorising his release still exists in the papers of the Adjutant General's Department, in
series WO 162 but it would take a a very dedicated researcher to trawl through the 383 files of correspondence to see if it had been retained.
The
Royal Hampshire Regiment Museum holds a number of records of service, regulations, order books, diaries, courts martial books, letter books for the period 1773-1956 which may just possibly include a reference to Pte Coleman's case.