Looks like it maybe a cuphea llavea. Thanks for pointing me in the right direction.

It is mainly an environmental weed especially on moist sites when I lived in Melbourne I pulled up and binned then all. They tend to take over the garden after a while. Here is a link that might be useful: Watsonia : Environmental Weed.

Without seeing the full cactus and flowers it's hard to tell, but my guess is Epiphyllum oxypetalum aka Queen of the Night. I find Epiphyllums one of the easiest to propagate. Just bury in some mix and leave be. Keep warm and in bright filtered light. No need to water till roots form. If you have a bathroom with a window. I would keep this in there. The humidity may help to kick start with the roots. The bathroom should have a window so there's airflow and light. These guys can get fungus. Normally for other cactus I wouldn't suggest this, but these are different.I've found roots usually pop out fast within a couple weeks. If they take longer it's fine;). You can water when roots form. No harsh sun for these guys. Like I said just nice bright filtered light. Remember these are rainforest cactus. Make sure to keep the mix fast draining so no soggy soil. My Epi mix is about 30% pumice, 20% perlite, and the rest cactus mix. Maybe your friend can let you borrow some of their mix. What hardiness zone are you in:)? Really helps when giving advice.

I was just looking at Sedum pics and came across what I think may be your plant. Check your original post.