The key of succesfully moving a plant or tree is less stress on the plant. To transplant trees in fall means comfortable temperatures and more. The best time of the year to transplant plants, definitely is autumn. This is because of cool temperatures and warm moist soil. Plants also require less energy as they begin to enter the early stages of dormancy. they are not focusing in above ground growth. This is perfect for root establishment you are wondering.
When you transplant trees in this season it gives your plant plenty of time to be thoroughly established and ready for the heat of summer. So, you will be allowed to see growing all the flowers that bloom in Fall.