In my view Trilliums should only be lifted and transplanted when absolutely necessary and I would prefer to do so as soon as growth commences in spring. For an alternative this year as spring has passed I would do so in mid to late autumn or wait until the following spring.

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I plant them any time from spring to fall except for hot sunny days.

I have transplanted a lot of trilliums from our woods into the garden. I usually do it right after they finish (or almost finish) blooming. Just be sure you get a big root ball. They have sort of fragile roots. If I wait until fall, I can't find them because they go dormant. I've found that you can even transplant them when they are still blooming if you dig up enough soil around them.