My apologies if this is a repeat question. I've searched for a while now but haven't come across an answer.

This is my dilemma:

My company is using a piece of software that has a 'sender address'. This address needs to be added to the users' mailbox in the 'Send on Behalf Of' field. Is there anyway to automate this process? Can I make this happen through a GPO or a security group or something? It would be very tedious to have to do this for every account and every newly created account.

Thank you for your help! 

Hello. Please look in the direction of the transport rule and their capabilities.

Exploring Transport Rules in Exchange Server 2013

Maybe I'm missing something here but looking through the Transport Rules... I don't see a feasible way to add 'Send on Behalf Of' permissions to every mailbox. Can you clarify?

Not all ideas are possible. :(
I think it's very simple script for PS Exchange, c planned launch times a day.

$DistinguishedName = Get-DistributionGroup MyGroup | Get-DistributionGroupMember
$DistinguishedName | ForEach-Object {Set-Mailbox -Identity user_mailbox -GrantSendOnBehalfTo @{Add = "$_"}}