Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. Since we do not have all the facts, it is impossible to give a completely accurate answers. What's his criminal history? When he got in trouble after the 1st conviction, what was he charged with? Why was he in jail in Jamaica? I strongly suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your husband's situation. (S)he would then be in a better position to analyze his case and advise you of his options.
Answered on Dec 02nd, 2014 at 9:01 PM