Braham of Boston calls 4.7.1802 In Godwin's 1796 list for 1802 / 17.2.1820 Theatre, Braham / 9.8.1834 Braham dies (crossed out)
The only reference I can find to a possible Braham of Boston was in the Morning Post of 21.8.1806 where it was said that Dr Erskine had been appointed minister to the US congress and set off last Thursday. "The same day Mr Braham quitted London on a mission to the court of Lisbon". This suggests to me that Braham was the name of an American consul but I can find no other reference to him. The Braham at the theatre in 1820 was John Braham DNB 1777-1856 but whether the crossed out "Braham dies" in 1834 meant him remains a mystery.
A Philip Braham lived at Gloucester Pl, Portman Sq in 1811 and at St Marylebone on 17.2.1807 a John reputed son of Philip Braham was baptised. I don't think he was from the US but the son of Wotton Braham of Edwardston Suffolk surgeon PCC 1771and he had been Acting Deputy Governor of Fort St George, Madras, he died in 1824 age 70 (Jackson's Oxford Journal 22.5.1824) his will PCC 1824. Farington's diary vol II p560 mentioned a Braham apothecary of Argyll St. A William Braham was an oil and colourman of 74 Snow Hill Holborn in 1790