Answer: Mimosas are better planted in the spring, this allows them to become well rooted before the stress of winter sets in. I am not sure you will be able to move the offsets successfully because their roots tend to deep and brittle.
If you want a new tree, you might try collecting some seedpods later this fall and setting them on prepared soil in the spot where you would like the tree. With luck, they will germinate next spring.
Otherwise you could try transplanting tiny seedlings early next summer. Most trees will self sow nearby, and if you can move a seedling when it is just an inch or two tall (take a large shovel full of soil with it) then it will not know it has been moved and should transplant perfectly.
Good luck with your mimosa tree!
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