The Alert Inbox provides a central view on all alerts which have been generated by the different Technical Monitoring scenarios on SAP Solution Manager. The generated alerts can directly be handled in the Alert Inbox or forwarded to other channels like incidents, email, SMS or even 3rd party applications.
Here you can check and navigate to all the alerts generated. There are also specific tab for each use case as Self monitoring, PI Monitoring alerts, etc. It is possible to confirm the alerts, so it will not appear here anymore. Then to find this alert after confirming it, you will need to navigate to "Alert Search" tile on the Solution Manager Launchpad. Drilling down by the parameters given will let you find the alert. Also confirmed alerts appear here.