After winning about $3.5 billion in default judgments against the Republic of Cuba, Fidel Castro’s persecuted political opponents and their families have cleared a hurdle in their bid to seize frozen Cuban assets at global banks including Spain’s Banco Bilbao Vizcaya Argentaria (BBVA).

In a ruling issued on Friday, U.S. District Judge Alvin Hellerstein in Manhattan denied BBVA’s request that he dismiss garnishment litigation the families brought in an attempt to collect on the judgments in New York. BBVA’s lawyers at White & Case argued that judgments issued against Cuba by courts in Florida are void, and that therefore Hellerstein lacks jurisdiction over the follow-on proceedings. But the judge disagreed, writing that the Florida rulings are entitled to deference.