One shared mailbox with multiple distribution groups connected and the sent items folder - how to configure?

Hi!

I have been struggling for a while now with the following issue.
For starters:
We are using exchange 2010 in combination with outlook 2013 on client computers.

Cause of the limitations concerning the number of mailboxes in outlook im looking for a solution to receive and reply 
to multiple aliasses. So i did the following:

1.Configured one shared mailbox.
2. Configured multiple distribution groups
3. made the shared mailbox a member of the distribution groups
4.Configured full access and send as permissions for myself on the shared mailbox ( testing )
5.Gave send as permissions to the shared mailbox in Active directory. 
6. Logged in to OWA to setup rules for the shared mailbox.

I now receive emails from all connected distribution groups in the shared mailbox and also in the right folder.
I do however have to select the proper from address when i reply to an email. 
the email sent by the main SMTP of the shared mailbox is placed into the sent folder of the shared mailbox. 
I setup the senddelagate blabla in register.....
When i sent an email as one of the connected distribution groups it fails to put the sent item in the sent items folder of the shared mailbox. The email is sent using the proper address but placed in the sent folder of my main account. 
I want this emails to end up in the sent items folder of the shared mailbox. Or even better, in a sent items folder for each of the addresses. 

Any suggestions ? 

Thanks in advance!