it does kind of look like coleus...i thought they were more of a bushy type plant
rather than viney tho...
there are a lot of varieties tho, so there may be some that are vining.
are you getting water on the leaves? water droplets on leaves that are getting full sunlight can cause burns to the leaves (the sunlight is magnified through the water droplet).
it's also possible that this isn't coleus and that it's just getting too much light. where does your friend have their plant
? you might try duplicating the light conditions and see if things get better.
also, if the roots are well formed enough at this point, you can plant
it in soil - there are some plants
that don't do too well if kept in plain water for too long.