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I am sorry for your loss, first of all
This is a good question. US Letters of Testamentary/Administration are not recognized outside of US jurisdictions. As such, the Executor in USA does not have an automatic right to conduct business and wind down/distribute assets on the estate's behalf in Jamaica. Technically, the Executor would have to file for probate in Jamaica to get a Jamaican equivalent of the appointment of Executor.
This may be the same Executor as the USA of course, or the parties can try to argue for a different Executor (for some reason or another).
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