How is Elysia chlorotica classified as an animal capable of photosynthesis?
Maybe you are familiar with the endosymbiotic theory which hypotetisays that the mitochondria (and chloroplast) was a little procrayote that got absorbed by larger organisme. At the beggining they were independent in an endosymbiontic relationship but in the process of evolution they merged to one organism from which all eukaryotes (plants). So yes, the process your describe is possible.
If it happens than the new organism is no longer E. chlorotica but a another which evolved from it, this creatue will likely still be clasified as an animal since there are non-photosynthetic plants and there are photosynthetic non-plants (algae, cyanobacteria), Therefore photosynthesys is not the definition of a plant.
The goal of the tree of life is to draw the &quot;familiy tree&quot; of all the living creatures. So, if we know one creature is an animal that gave rise to another one with a special ability we will still clasify it as an animal.