Someone got the boot from a supervisor which clearly was not informed of the actual work of the employee (all the reasons for termination/forced resignation where one-sided and didn't really stand to evidence). This supervisor has a supervisor. Should the employee just keep his evidence of a misinformed decision to himself and walk away giving thanks for the time there? Or should they write a letter to the higher-ups informing of their work and how this event didn't make sense/was uncalled for?
Edit: This is in US