We cannot update Messaging User Account and Messaging User Contact on the Messaging Session. They are read only and not writable.

Only Case, Lead, and Opportunity are editable.

If you would like to update the Messaging User Account and Messaging User Contact on the Messaging Session, then update the Account and Contact on the Messaging End User record. 

Messaging Session:

Messaging User:

Account and Contact in Messaging User is used in Messaging Session.

To update these fields:

1. In the below Messaging Session, the Messaging User Account is Test1. This is coming from the Messaging User’s Account field. 

2. Open the Messaging User record. Check the below screenshot.

3. Now, I am updating the Messaging User’s Account to Sample. 

4. Now, refresh your browser and check the messaging session record. Its Messaging User Account will be updated to Sample.