The easiest thing to remember is: hey, don’t worry, because this will never come up. Trilliums are well dormant before Jack-in-the-Pulpit (Arisaema triphyllum) becomes interesting, and most people don’t go around dividing trilliums (you totally can though* – do it when you can find them, when they are in flower. If they promptly go dormant, if you have put them in a place where they will be happy, you’ll see them again next year.)
But. If you are scratching around for trilliums in September because you have it in your head that a trillium/Jack-in-the-Pulpit bed might work since they like similar conditions you might be able to find a few in their most sheltered spots, near water, in dark areas under trees. They transplant remarkably well, though once they are dug I would expect them to promptly pass out and spend the rest of the season in dormancy.
I found a few a couple of days ago and dug them up and should note that these were existing on our property, not in the wild, and that I’m not moving entire successful populations here – these divisions increase the population of those species on land where they already live. I’m not poaching native species! Don’t do that; it’s bad. And also usually illegal.
We have mostly red trillium here (Trillium erectum) but also a few white ones (Trillium grandiflorum).
I’m not sure which I recovered and didn’t take a picture, the leaves were yellow, the long-dead flower hanging on to a stem clearly questioning what it was doing out of bed in September, but the rhizomes were white and healthy, and I swear: it’ll be fine.
Anyway: the ID secret? Veins on the leaves. The veins on trilliums are more complex (I think they are considered palmate because the veins look like outstretched fingers on a hand.) Jack in the Pulpit leaves are much sympler – bifurcated and symmetrical–see the second photo.
And here is where I learned to be brutal with trilliums.