Best to wait until at least after the bloom cycle. Like many plants in this family, they are fairly surface rooted so a shallow and high planting method is warranted. Keep well watered and mulch to conserve soil moisture.

My mountain laurels are just pushing out new foliage now and will be blooming soon, so if it is possible to do it later in the year I would wait and move it in late August/early September when the soil is warm but the days will be shorter and starting to cool off. That will give it time to settle in before winter, but save it from heat stress this summer.

And be ready t. provide temporary shade