The below is a work in progress, but gives you the recipe if you need to enhance the transaction search for a custom field.
One of our long-standing requirements, since we have been using CRM 40 is to integrate fields generated by the EEWB into the business transaction search. In the new CRM webclient we found we can do this, however it is once again a manual procedure.
Step 1: Identify the search structure using GENIL_MODEL_BROWSER
Step 2: Enhance the structure in SE11
Step 3: Implement the BADI CRM_RF_SEARCH_EEW
Step 4: Add entry to CRMC_REPDY for the field
Step 4a: If you are upgrading from CRM 5.0 to 7.0 then you have to set the Checkbox "No hiding of fields by design layer" in the Customizing at CRM -> UI Framework -> UI Framework Definition -> Design Layer -> Deactivate Hiding of Fields
Step 5: Add field to search view in CRM webclient
Step 6 Optional: Add input help for the new search field
This proved be very easy once the method to create the enhancement was determined. It would have been nice if there was a "migrate option" in the EEWB that could have generated this for all our existing objects.
See also document "How to Integrate a New Search Attribute into the Agent Inbox "