As you seem to have already discovered, his service record doesn't appear to have survived. This was quite common for soldiers who didn't serve for long enough to qualify for a pension. The Army had no reason to retain their records once they had been discharged as fit.
I have been unable to find out a great deal about F Battery, B Brigade RHA during the time you are interested in.. The first thing to say is that it has no connection to today's
F (Sphinx) Parachute Battery RHA. That battery traces its roots back to A Battery B Brigade.
What I can tell you is that
B Brigade was formed in India on 13 April 1864 out of the old 1st Brigade RHA. Its original composition only consisted of batteries A - E. F Battery was in C Brigade, with its antecedents as 1st Troop, 3rd Brigade Bengal Horse Artillery first raised at Sialkot, part of the Armies of the East India Company. There was a further reorganisation of the RHA on 14 April 1877, during which F Battery transferred to B Brigade. F Battery does not appear to have been involved in the Second Anglo-Afghan War 1878-1880 and probably returned to the UK in about 1881 or early 82 as they are located at Aldershot by August 1882.The battery remains in Aldershot until 1885 when it moved to Canterbury, and around the time that Joseph is being discharged in December 1886, the Battery was located at Abbassiya in Egypt (see press cuttings below).
The reason that Robert was discharged was, as you say, because he lied about his age when he enlisted on 7 May 1885 (he would have been aged 15 at the time). Perhaps he joined at the same time as his brother Joseph who would have been around 18 or 19. But in any case, unless he also lied about his age Joseph wouldn't have been able to join until he was 18 since the Royal Horse Artillery didn't recruit boy soldiers at that stage. That means that his discharge in December 1886, shortly after his brother Robert was discharged in September, is distinctly odd. He could only have served for perhaps at most two years, which is considerably shorter than any engagement at the time. So either he too lied about his age and was discharged, or he was found unfit for further service, or possibly, he bought himself out. The cost of buying himself out would have been around £10- an enormous sum in those days. I don't think he will have seen any active service and I suspect he didn't leave the UK during his brief career in the Army.
