Hello and welcome to the forum. Firstly, I have to ask you if you know for sure that your man was definitely in the army and fought in the Boer War and, if so, that he died in the war. Murphy isn't an uncommon name especially with army connections of the period because of the number of Irishmen who served in pretty well every regiment.
There are 13 Murphys listed in the casualty roll of whom 4 died. One of these is 4055 Pte. W. Murphy of 1st battalion Manchester Regiment. The battle of Talana was fought on 20/10/1899 but the casualty roll is incorrect in listing him and other men of the battalion as casualties of the battle as the Manchesters weren't there. He was in fact killed at the battle of Elandslaagte which was was fought the day after. He was entitled to the Queen's South Africa Medal with clasp Elandslaagte.
I have a copy of the battalion's QSA Medal roll and there are several Murphys listed including 4151 Pte. W. Murphy who was awarded the medal with clasps Natal and Transvaal and was transferred to 19th battery Royal Field Artillery where he may well have earned additional clasps. Overall there would have been dozens, if not hundreds, of W. Murphys serving in the army at the time.
Regular soldiers' service papers of the period are in series WO 97 at the Natonal Archives in Kew. However, the papers of men who died on service no longer exist as they were officially destroyed about 90 years ago.
Also. being born in Manchester doesn't necessarily mean that a man joined the Manchester Regiment. Many men did join their local regiment but equally many did not. Among these were men who joined the various corps (engineers, artillery, etc.) as well as other regiments. For example I have the medals and papers of several men of the Gordon Highlanders who fought in the Boer War. Not one of them was from the highlands and only one was even Scottish. Others came from York, London, Surrey, etc.
The conclusion of all this is that to progress your research you'll need more information to start with.
David