That's a new character, so it's almost certainly not a timeskip. There's no clear indication of there being a timeskip, either.
Anyhow, Anderson's Little Mermaid doesn't just turn into sea foam-- she turns into sea foam because she refuses to kill someone in order to not die. Because of that virtuous decision, though, she becomes a wind spirit after her death, and is responsible for making children happy for three centuries before she's given a soul and allowed to enter Heaven, with the proviso that crying kids add to that time limit and happy kids subtracts from it.