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If one does a Full Profile Backup and Restore with Febe then all the styles as well as Stylish will be restored in the New Profile.

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If you use Febe to simply copy your extensions then it will not copy the Styles.

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However I have learned from Mafia_Penguin the following regarding Febe :

Go to Tools>FEBE>FEBE Options
Click on "User-defined backups".

Click "New".
Fill out the information, and check "Include in backup". Click "Post entries and exit".

This is a useful procedure

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If you want to recover your styles from an otherwise corrupt profile, it is quite sufficient to do the following.

1. Look for the file stylish.rdf in the Profile you want to copy FROM.

2. Copy the contents of the file in 1. into your stylish.rdf in the Profile you want to copy tp, being careful at the same time to remove the previous contents

This system can save a lot of work, as many Styles may also have been customised.