Cut the end, let it dry out a few days and put it in some cactus/succulent mix. Should do the trick.

It is probably good that it broke - it is etiolated. I would probably make shorter stem cutting and root it. If any extra leaves, you could try to root them too. Photo is not showing plant well enough for me to make any more suggestions.

whenever you have some heirloom precious plant.. you should propagate it.. and have 2 or 3 around.. just to secure the future ...

and once you get the ID... learn how to grow it to perfection .. this one is not in good shape ... and you can do better ...

and then take the ID to a seach.. and add the word propagation ... and then ht videos.. and you should be all set ...watch a couple.. and then do what you gotta do ...nerves aside.. it shouldnt be a big deal ...

note the above answer.. do not put them in a glass of water.. while you gather up what you need ...

ken