To see permissions on a mailbox:
Get-MailboxPermission -Identity User| where isinherited -eq $false
Snippet to add permissions:
Add Full access:
$MailboxPermission = @{ 'identity' = "Bob Harris" 'user' = "Bill Goat" 'AccessRights' = 'FullAccess'.'DeleteItem' 'AutoMapping' = $true } Add-MailboxPermission @MailboxPermission
Possible permissions: FullAccess, SendAs, ExternalAccount, DeleteItem, ReadPermission, ChangePermission, ChangeOwner
To Remove Full Access:
Remove-MailboxPermission -identity "Bob Harris" -User "Bill Goat" -AccessRights DeleteItem -Confirm:$false