The year 1655 was a time of great opportunity for Sephardic Jews - Spaniards had to leave Jamaica, but resident Jews could stay (presumably by shedding their New Christian disguise) and new Jews could arrive as their trade was generally encouraged both by Cromwell and Charles 3.
Jamaica must have been a particularly hospitable place for the New Christian merchants. In fact, according to Roth (ref 15), in Jamaica the Inquisition never obtained a footing, and he confirms large numbers of Portuguese New Christians were there before 1655. The Sephardic community in Spanish Town welcomed the prospect of English rule and variously assisted the English forces under Penn and Venables which took the island in 1655 though of course this was not militarily contested as the Spaniards had long since lost interest in favour of 'The Spanish Main' and their West-East shipping lane moved to the north of Cuba thereby enhancing their neglect of Jamaica. The pilot upon whom the English captors Penn and Venables relied, Campoe Sabbatha, is said to have been one; another, Acosta, superintended the commissariat for the English troops and negotiated the terms of capitulation; while Simon de Caceres, the 'chauvinistic Jew', in London, furnished much valuable information. Larger landholders became wealthy and merchants in the ports prospered. Some 20 years after the English capture numbers rapidly increased. This was achieved by immigration from Holland and England; and also Brazil and Surinam when those colonies changed hands; and also kin of the Cree Church (later Bevis Marks) congregation. They had to pay special taxes but the greater part of the trade was in their hands. This detail comes from Hyamson.
The position was not completely rosy! Arbell (ref 14) notes the 30 Aug 1692 petition from Jamaica to William and Mary for endenization, following the devastating 7 June earthquake there, by Isak Moses Barak and his co-signatories who were Isaque Fernandes Diaz, Isaque Nunez, Phineas Arbarbanel, Isaque Rodriguez de Souza, Aron Jacob Soarez, Jacob de Caseres, Jacob David de Robles, and Isaque Mendez Gutierez. Patents of Endenization were granted (see ref 42) to only two gentlemen with names corresponding to names on the list (Dias on 9 March 1694, and Arbabanel on 3 June 1699) rather than all of them as would almost certainly have been the case under Charles 2; his discussion points on the other hand to the petition being the start of special taxation for the Jews of Jamaica - including personal payments to the English Governor - whilst pointing to their lack of voting rights. It was not until 1831 that the Jews had full civil rights in Jamaica. The name Isak Moses Barak probably (in accordance with Sephardic naming tradition) means Isaac son of Moses Baruch.
However as Edgar Samuel (ref 35 chapter 21) pointed out, Jamaica in the 1700s was very favourably positioned to profit from trade with the Spanish Main.