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Yes, a letter should be written to resign. It can be quite simple. For example:
RESIGNATION OF OFFICER
I, ________________________, hereby resign as __________________ of ____________________________________________, Inc., to take effect immediately.
It also appears that she wishes to abandon the shares she was issued in the corporation. She should return the share certificates to the corporation with another letter simply expressing that, as well. Just replace "resign" with "abandon the shares enclosed" or something similar.