Authorities shot and killed the alligator to stop it from doing more damage to the remains.
After the animal was killed, a diver went in the water to recover the remains from the dead alligator, officials said.
Their investigation will also determine if the alligator killed her or if the animal was scouring her remains after she was already dead.
Eight months ago a similar incident happened in Largo, Florida.
Officials there shot and killed a 13ft (4m) alligator after they found it walking along a street with a torso in its mouth.
The remains were later identified as that of 41-year-old Sabrina Peckham.A few months before that a 10ft alligator killed an 85-year-old woman in Fort Pierce, Florida as she was walking her dog.
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