TACA does it, but it's awfully convoluted and quite expensive.
http://www.taca.com/You fly Roatan to San Pedro Sula on a commuter flight at 10:00, arriving 10:55. Then at 13:00 on regular flights from San Pedro to San Salvador, then to San Jose, Costa Rica and finally to Havana, arriving at 22:55. The fares seems to be about US$ 550.00 single.
Any travel agent on Roatan will be able to help, or perhaps the TACA office there.
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