Darryl

Sorry for your loss – this is a very lovely, well-cared for specimen!

Think about the place where this plant lived – think specifically about the size of the window(s), the plant’s proximity to them, and the number of hours when the sun would come into direct line of sight with the plant. If at all possible, try your best to replicate that lighting situation. If your best possible lighting situation (by which I mean, the widest possible view of the sky plus the number of hours of direct sun that is tolerable by this plant – which is 3-4 hours through a glass) won’t be as close as what it used to be, then the plant will gradually adjust to your light situation by losing a few of its older leaves BEFORE growing any new ones. These trunk-type philodendrons (which are now classified as Thaumatophyllum) only hold on to the top group of leaves as they grow. The total number of leaves held onto in this group is mostly dependent on the balance of (1) good lighting (even and diffused all around), (2) adequate watering (water when partially dry), and (3) sufficient soil nutrition.

The lowest leaves will always fall off. Don’t fall into the trap of trying to diagnose everything:

“An experienced plant parent is not the one who never loses a leaf, it’s the one who knows how much leaf loss is normal.”
~ Darryl Cheng @houseplantjournal

Thaumatophyllum plants do not propagate the same way that Monsteras do. I wouldn’t try taking a cutting from the trunk. I think you should leave them together.

Darryl

Is there any way you could find out how the previous owner fertilized the plant?

If not, I’d recommend any balanced fertilizer or something with higher nitrogen (the first number in the three numbers of fertilizers: NPK). Most come in liquid form and you just add a few drops to the water used for watering (use as directed or dilute slightly weaker).