Decommissioning old exchange email from SBS 2011

We have recently migrated our clients email service from Microst exchange which was hosted on their local SBS 2011 server to Microsoft hosted exchange. They are now receiving external emails to their email addresses (which are being accessed through Office 365 online web access) but are not receiving their internally sent emails which are sent from the same domain name. Internal emails are still being received by the old exchange service on SBS 2011. We just want the old exchange to stop bringing in internal email and allow the new hosted exchange to receive it and allow us to set up the new email accounts on their work stations.