If the tree is not too large it can be moved. Otherwise it is not practical to do. The best time to dig up and move a tree or shrub is in November. By then the cooler weather will be shutting down the plant as winter approaches, reducing the immediate shock of transplanting in warmer weather. It also allows the maximum amount of time for the roots to establish in their new location, before the onset of hot weather the following spring.
Dig the plant, trying to make sure and get as much of the root system as you can. Tilt the plant to one side and slide a tarp beneath the root ball. Then tilt it the other way and slide it onto the tarp. Use the tarp to drag it to its new location (this prevents lots of back strain). Plant it at the same depth it was growing before, and water it in well as you firm soil around the roots. Maintain moderate soil moisture but not too soggy wet for too long.
Eucalyptus prefers a sunny location.
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