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Can I have functionality like email back when stock is available?
This functionality is already available.
The only difference is that the customer must have an account and be logged in before subscribing to this alert.
In order to enable it go to System->Configuration->Catalog->Product alerts and set ‘Allow Alert When Product Comes Back in Stock’ to ‘Yes’.
Clear the cache just in case, set a product out of stock and see what you can do in the frontend.
Yes, the functionality is build in magento. If you plan to use it intensively you might be interested in the Product Alerts Reports extension, as it gives you full overview of the alerts usage activity.