sorry to hear about your loss.

cut the rotted part off, leave the good part in shade for a day or two, till the cut has a chance to dry a bit. then stick it in a pot of dry potting soil/perlite mix. do not let it get wet until it has developed a few leaves.

Hi,
I would use a sharp knife and cut just above the mushy part until you get to good, clean wood. The inside of the stem should be white, and will probably ooze a little latex looking stuff. Let the cut end dry out for a few days and then pot it up again. Since we're having this June gloom weather here in L.A., I wouldn't saturate the potting medium with water (maybe, just lightly moisten the soil mix) otherwise your cutting will sit in soggy soil too long and will probably rot again. Don't water again until leaves form (misting the tip occasionally is okay, just don't let the water run down the stem). This is what I would do if it were my cutting, others may have a different approach. Hopefully, they'll join in and give you their thoughts.
Good luck,
Rick

I will try. Thank you for your help.