Hi Karen
I've found if you allow the broken end to dry and then plant the broken end.................it grows but may still end up rotting at the broken end..........................so the best way I feel is to lay it flat and bury those air roots ......keeping the cut end out of the soil..................
Have you had any fruit yet?

Hello Marcy,
Thank you for responding. :)
No flowers or fruit yet.

There actually aren't any broken ends in need of drying: the woody stem (see photo in my first post, above) snapped away from the original plant beneath the soil line.
I hadn't considered planting the aerial roots I thought they were strictly for climbing?

Use a well draining mix in a pot suitable for holding the plant. Insert a stake into the mix. Tie the cutting to the stake with the broken end right at soil level. Spray the surface of the soil on occasion with a mist of water. Eventually roots will form at the broken end.
Alternatively, you can simply place the entire piece in a emply clay pot large enough to avoid toppling. It may take weeks but it will root. This plant has a tenacious hold on life and a desire to live and grow. I once had a piece that laid on the bench in the greenhouse for months and it rooted and started growing up the wall, clinging to the side with air roots.

If you are into grafting they make excellent grafting stock for cacti that are difficult to grow on their own roots.

Thank you to everyone! I'll keep you posted on how it goes!