Answer: This could be a rather large undertaking, given the size of the tree. It would also be a bit of a shock for the tree to move from shade to sun. These trees generally perform best in morning sun or in dappled light all day, in a location with acidic, humusy soil that is evenly moist (yet not soggy), so it may not do well in full sun. This is especially true if it has been growing in deep shade for a good length of time.
You would want to transplant in fall or very early spring before the tree leafs out. This would minimize stress. If the tree has just recently been planted, it will be fairly simply to dig it up and move it since the roots should still be close to the original rootball it had at planting. Replant at the same depth and keep the soil moist until it becomes established.
However, in my experience, to move an established tree like this really would not be a job for the homeowner but would instead require the services (and possibly equipment) of a professionally trained and certified arborist. Ideally, too, you would begin a year ahead of time by root pruning the tree to encourage roots to grow closer to the trunk to facilitate reestablishment after the move.
A tree's roots typically spread at least as far as the branches, and usually further, some times as much as half again as wide. Japanese maples are shallow rooted, so you might only have to dig down about a foot. However, the root ball would be unwieldy and extremely heavy and difficult to move successfully. If this is an established tree, I would encourage you to reconsider moving it or at least consult with an arborist for an on-site opinion as to the chances of success.
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