If you are getting an INVALID_SESSION_ID error on the MassMailer Finish step, you may have to check the following settings and make changes to the same.
DIAGNOSTICS 1
Navigate to your Profile -> Session Settings -> Make sure that 'Session Security Level Required at Login' is BLANK OR NONE.
DIAGNOSTICS 2
Navigate to your Salesforce Setup -> Session Settings -> UNCHECK 'Lock sessions to the IP address from which they originated' OR 'Lock sessions to the domain in which they were first used'
