Hello,
I'm sorry but may you please elaborate a little bit on your requirement? Because usually you want to notify a user when errors occur (not when Bdocs are correctly processed...). So there is nothing in SAP standard delivery to achieve your requirement... and if you really need it, some modification to SAP coding will be necessary, with a tricky part: find a way to notify the user only when a Bdoc is correctly processed after the first try (because you certainly do not want to notify someone for every Bdoc that is correctly processed without going first into error).
Regards,
Nicolas.