Did you ever hear the saying, "The best time to prune a plant is when you have pruners in your hand."? I sort of live by this saying when it comes to moving plants. The best time to move a plant is when I'm in the mood to move. That is usually not in the middle/heat of summer just because it can be a real undertaking to move established plants. That is also not in winter or too close to winter.

Other than that, I move when it's convenient for me. I always treat new plants with a bit of special care which includes: adding Biotone to the hole, then watering them daily, and I give them shade for a couple of weeks using an umbrella or shade cloth above them somehow. Tomato cages work good for this as do these laundry baskets upside-down of course and secure it to the ground with landscape staples.

Oh and I prepare myself for the fact that the moved plant may / may not bloom the following season as it devotes its energy to root growth.