An investigation is now underway to determine if she was pushed over the railing.
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The FBI is leading the investigation after the Princess Cruises ship returned to Fort Lauderdale on Saturday.
According to local news in Aruba, the woman fell after arguing with a man and landed on a lifeboat.
ABC News confirmed the identity of the victim as 52-year-old Almarosa Tenorio, who was on a vacation with her husband.
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They say he is not a suspect in her death.
Tony Rodriguez, Tenorio's brother, confirmed the death of his sister and sent the following statement:
"Almarosa was a very loving daughter, sister, mom and grandmother with a good heart," he wrote. "Her passion was teaching and working with children. She had a vivacious personality with a smile that would light up a room. We are sad that she was taken from us at such a young age. She will be missed by all that knew her."
The Royal Princess departed Nov. 9 from Port Everglades on a 7-day Southern Caribbean cruise.