Yes, Claimable can notify you via email when a note is added to a claim. You can choose between being notified for notes added on all claims or for notes added only on claims assigned to you.
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You will just need to have either the "Note Added (All Claims)" or the "Note Added (Assigned Claims)" notification turned on for your user account.

To do so, open the Notifications tab under Your Preferences and tick the box next to the preferred option.

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