Answer: Your Southern Magnolia is about half-grown and will grow equally well in a partly sunny spot as it will in one that receives full sun. If you want to move it only because of the exposure to shade, it won't be necessary. Although it has been in the ground for six years, it may have taken 2-3 years for the root system to become established before it was ready to put out lots of new top growth. The winter damage it received probably set it back some, too. I'd leave it where it is and do some pruning to balance the branching system out, and to encourage healthy new growth.
If you decide to move it, winter or early spring is the best time. Expect the root system to be quite extensive (growing well beyond the canopy). Sometimes trees react well to transplanting, other times they can take 2-3 years to become re-established. It all depends upon how distressed the root system becomes during and after the move. Prune it in late winter or early spring at the same time you move your tree.
Best wishes with your landscape.
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