Hi Mathew,
To add the Status 'Send to Distribution' in Inbox Search page
SPRO--> CRM-->Interaction Center Webclient-->Agent Inbox-->Inbox Search Definitions -->Define Inbox status
If you want to add the status 'Send to Distribution' to a transaction. first you need to add the status to the status profile of the Transaction Type
Step 1
SPRO-->CRM --> Transaction --> BAsic Settings --> Status Managment-->Define status profile for user status
Step 2
SPRO-->CRM --> Transaction --> BAsic Settings --> Define Transaction Types
With Regards,
selvam