This is a question which I have been researching for quite some time.
The FP BG mark actually refers to a B. Goss, probably Benjamin. As you say, they worked together earlier. I've found no records of a silversmith by that name in Exeter although there was a cabinet maker. I think it's most likely that he was simply a business partner to Francis Parsons, playing no role in the actual manufacture of silver items.
Joseph Goss, the G in the G&P mark, was apprenticed to a clockmaker in 1779, a trade connected with silversmithing. He worked with Francis Parsons from 1810-1814. I haven't been able to verify that he was related to B. Goss, but since they were apprenticed within five years of each other, it's likely that they were brothers.
This is from a local newspaper in September 1814: “Notice is hereby given, that the partnership lately subsisting between Joseph Goss and Francis Allen Parsons, of the city of Exeter, Working Silversmiths, was this day dissolved by mutual consent. All persons having claims on the said partnership, are requested to deliver their accounts to Joseph Goss, at his house on Northenhay.”