She is double boosted but the SXM entry requirements do not read that way. They simply state and do not seem to indicate vaccination eliminates this requirement:

Travelers who have recovered from a Covid-19 infection within 9 months before departure must upload one of the below acceptable proof of recovery:

A government / public health authority issued proof of recovery (Digital Covid Recovery Certificate or letter)
A lab issued positive covid-19 PCR test result also indicating a Ct value of 35 or higher.
A signed and stamped Covid-19 recovery letter from a physician accompanied by the positive Covid-19 PCR test result.

If I am misreading something, please let me know. https://stmaartenehas.com/travel-requirements/