Lithium batteries cause all sorts of kerfuffle with couriers and airlines these days. EPS is notorious for seeing a battery and putting the breaks on. The last time I had a gizmo shipped to me that contained a battery, I had to supply MSDS info, and point out from several sources that the neither the device nor the battery is considered a dangerous good. Still took about six weeks to work it out.
This battery has to be available somewhere on the island, it's just a question of finding where. Must be available in SD, Santiago and probably POP. If I can't find one locally, then I'll widen the search even if I have to pay someone to toss it on the bus. The battery powers an alarm sensor.
Possibly a camera store or an electronics place.