Windows Exchange 2010 - grant folder access in Outlook 2010

you can refer the article -

https://technet.microsoft.com/en-us/library/dd298062(v=exchg.141).aspx

EXAMPLE 1
This example assigns permissions for Ed to access Ayla's Marketing mailbox folder and applies the Owner role to his access of that folder.
Add-MailboxFolderPermission -Identity ayla@contoso.com:\Marketing -User Ed@contoso.com -AccessRights Owner

Also you can refer

https://technet.microsoft.com/en-us/library/aa996343(v=exchg.141).aspx

here is the script that I use to grant a user read-only access to existing mailbox.

###################################
# Grant read-only access to user mailboxes       #
###################################

#Defined User Inputs

$Mailbox = read-host -prompt "Enter username of the mailbox that needs to be accessed"
$User = Read-Host -prompt "Enter username of the person that requires access"

#Granting Review Rights to mailbox

Write-Host -ForegroundColor Green "Granting $User $Access Rights to $Mailbox mailbox at the top level"

Add-MailboxPermission -Identity $Mailbox -User $User -AccessRights ReadPermission -InheritanceType all

Start-Sleep -s 30
Write-Host -ForegroundColor Yellow "Granting $User Reviewer Rights to $Mailbox all mailbox folders"

$exclusions = @("/Sync Issues",
                "/Sync Issues/Conflicts",
                "/Sync Issues/Local Failures",
                "/Sync Issues/Server Failures",
                "/Recoverable Items",
                "/Deletions",
                "/Purges",
                "/Versions"
                )



$mailboxfolders = @(Get-MailboxFolderStatistics $Mailbox | Where {!($exclusions -icontains $_.FolderPath)} | Select FolderPath)

foreach ($mailboxfolder in $mailboxfolders)
{
    $folder = $mailboxfolder.FolderPath.Replace("/","\")
    if ($folder -match "Top of Information Store")
    {
       $folder = $folder.Replace(“\Top of Information Store”,”\”)
    }
    $identity = "$($mailbox):$folder"
    Write-Host "Adding $user to $identity with Reviewer permissions"
    Add-MailboxFolderPermission -Identity $identity -User $user -AccessRights Reviewer -ErrorAction SilentlyContinue
}

Select all Open in new window

If the you need to forward the new emails to a designated employee you can do that from the EMC, Mail Flow Settings, Delivery Options. and send all new email to designate