it would have been nice if the article suggested some means by which the sea slug took the genes in. There are many ways horizontal gene transfer is accomplished. In order to actually incorporate it into the host genome, a vector such as a virus is usually used.
From a generic viral life cycle, host cells are used for reproduction: restriction enzymes cut host genetic material and whatever is close enough to fitting the "sticky" ends attaches, intentionally the viral genetic data, but can be other stuff (success is based on probability). In order for it to pass to the next generation it would have to happen in a sex cell though (since sea slugs don't reproduce by budding).
the genes for maintaining chloroplasts, and as per the article making chlorophyll, were probably transferred many generations past
http://en.wikipedia.org/wiki/Restriction_enzyme
http://en.wikipedia.org/wiki/Elysia_chlorotica
as per wiki, the sea slug needs to ingest algae every ~10 months, as that is the lifespan of the chloroplast in the sea slug.