If you are using the Kobo app on the device and the annotations are for books bought from Kobo, they should be synced automatically to Kobo's servers. Then they will sync to the new device. And they should sync to the Kobo Android or iOS apps running on other devices. And they should go to the Kobo desktop application on a Windows PC or Mac or a Kobo e-ink device.
If you are using another app to read, then you need to find out how it handles the annotations and see if there is a way to sync, or copy them from the device.
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