$User = "i.meszely@aps-hh.de"

# Full Access
Get-Mailbox | Get-MailboxPermission | Where-Object { $_.User -like $User -and $_.AccessRights -contains "FullAccess" } | Select-Object Identity, User, AccessRights
# Send As
Get-Mailbox | Get-ADPermission | Where-Object { $_.User -like $User -and $_.ExtendedRights -like "Send As" } | Select-Object Identity, User, ExtendedRights
# Mitglied
Get-DistributionGroup | Where-Object { (Get-DistributionGroupMember $_.Identity -ResultSize Unlimited) -contains $User } | Select-Object Name, PrimarySmtpAddress