After a crash of an Exchange server it appeared unclear of how to use the "Mailbox Recovery" option of Exchange. The TechNet articles were not very clear an the recovery took more time than expected. For this reason the complete procedure which was successful is written down in this article.

Run the Exchange Powershell as Administrator.
In this example the servername is "EXCHSVR", the mailbox store is "C:\Program Files\Microsoft\Exchange Server\Mailbox\First Storage Group\Mailbox Database.edb" and the mailbox store to be recovered will be in "E:\RSG". We also presume that a copy of "Mailbox Database.edb" will be recovered.
The powershell command to create the Recovery Storage Group is:
New-StorageGroup -Server EXCHSVR -LogFolderPath E:\RSG -Name "RSG" -SystemFolderPath "E:\RSG" -Recovery
The next step is to create the recovery mailbox database. With this step no actual database is created, only a reference for Exchange.
The command for creating the mailbox database is:
New-MailboxDatabase -MailboxDatabaseToRecover "Mailbox Database" -StorageGroup "EXCHSVR\RSG" -EDBFilePath "E:\RSG\Mailbox Database.edb"
As you can see there is a reference to the existing mailbox database. At this point only the name of the database (Mailbox database) is sufficient, because this is the only database with this name. From now on the naming of the databases will be the full name.
At this point Exchange must know that the recovery database can be "overwritten" when mounted. The command is:
Set-MailboxDatabase -Identity "EXCHSVR\RSG\Mailbox Database" -AllowFileRestore $true
After this command the copy of the "Mailbox Database.edb" must be placed in "E:\RSG". When this is completed, mount the database:
Mount-Database -Identity "EXCHSVR\RSG\Mailbox Database.edb"
At this point you must be curious of the content of the recovery database. You can check the content with:
Get-MailboxStatistics -database "EXCHSVR\RSG\Mailbox Database"
This gives a listing of the mailboxes in the database and a restore action must be done with the "Display Name" of the mailbox. For Example:
Restore-Mailbox -RSGMailbox "John Doe" -RSGDatabase "EXCHSVR\RSG\Mailbox Database" -Identity "John Doe" -TargetFolder "MailRestore"
After a crash it can happen that the identity of the source mailbox is different then the target mailbox. For example, source "John Doe" and target "Doe John", because entering the userid in the Active Directory is different. The target folder will be created at the same level as the "Inbox" of the target identity.