Arbitration mailbox: Need to move before removing the database/server, can be created: Recreate missing arbitration mailboxes
Check by the following command:
Get-Mailbox -Arbitration | Fl Name, DisplayName, Database,Servername
Health mailbox(monirtoring mailbox): Don't need to move them, detailed information see here: https://techcommunity.microsoft.com/t5/exchange-team-blog/exchange-2013-2016-monitoring-mailboxes/ba-p/611004
Check monitoring mailboxes associated with a specific server/database by the following command:
Get-Mailbox -Monitoring | ?{$_.DisplayName -like "*-<servername>/<databasename>-*"}| Fl Name, DisplayName, Database,Servername
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