First, have you tried clicking on 'Save' in the top right-hand corner?
If you want to try saving your tree to your computer, follow these steps:
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On the family you want to back up, click on 'Download/export this family'.
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Select 'FamilyScript'.
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Click 'Download'.
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Save the file which downloads (I recommend in 'My Documents' or equivalent'). Make sure you give it a name you can easily recognise.
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Go to the account you want to export the tree to.
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Go to 'My Account', and click on 'Create or import new family'.
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Click on 'Import GEDCOM or FamilyScript'.
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Click 'Browse' and find the tree's file where you saved it.
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Click 'Import', and then 'Finish Import'.
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Save the tree on the new account (use the normal 'Save' button).
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You should then be able to use the tree as normal.
Steps 1-4 are fine if you just want a copy on your computer, but you can import it back into your account as a copy by following up to 11.
Hope this helps!