The best time for hydrangea transplanting is just after the bushes have gone dormant in the autumn. This means the flowers have all died back and most, or all, of the leaves have dropped. In climates where the ground doesn’t freeze, you can do your hydrangea transplanting between December and February. The active growth period for hydrangeas is March through September.  If your hydrangea bush is big and unwieldy, prune it back a little before moving it. Take care when pruning since bigleaf hydrangeas don’t need much pruning. Prune out a few of the oldest stems down to the ground each year, removing no more than one-third of the total stems in one year. Do this right after they flower in the summer. Don’t prune these in late winter or spring. Bigleaf hydrangeas flower on older wood, so pruning before flowering removes the flower buds.  Prune to the first leaf node of this year’s growth. Remember, the later you prune and the more drastically you prune, the fewer blooms you’ll have.

When selecting a new location remember right plant, right place. All hydrangeas will bloom and grow well in morning sun and afternoon shade. This is especially true of your plant, Hydrangea macrophylla, big leaf hydrangeas. Here are 2 references with complete information.

http://extension.oregonstate.edu/benton/sites/default/files/hydrangeashandout.pdf  

https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/transplanting-hydrangea-bushes.htm