Please refer to the following PowerShell Script to allow internal Application Servers / Printer to relay Email via Exchange 2010 / 2013
New-ReceiveConnector -Name 'Internal Relay for Printers' -Usage 'Custom' -Bindings '0.0.0.0:25' -RemoteIPRanges '192.168.2.40','192.168.2.41','192.168.2.42','192.168.2.44','192.168.2.45','192.168.2.46','192.168.2.48' -Server 'EX01'
#Allow AnonymousUsers to replay
Set-ReceiveConnector "EX01\Internal Relay for Printers" -PermissionGroups AnonymousUsers
#To activate Anonymous users to use this connector for relaying
Get-ReceiveConnector “EX01\Internal Relay for Printers” | Add-ADPermission -User “NT AUTHORITY\ANONYMOUS LOGON” -ExtendedRights “ms-Exch-SMTP-Accept-Any-Recipient”
Reference link