My mother has been diagnosed with a mental illness, Borderline Personality Disorder. She is constantly accusing me of stealing her money, which I have not done. I am getting exasperated. Can I actually forgive her? I ask because she probably is not giving full consent of her free will to these thoughts.

You raise an important point about whether or not we can forgive if there was no intention to harm.  I think it is appropriate to forgive in some cases even if there was no intention to harm.  Here is one example: Smith is not paying attention while driving and hits and seriously injures Jones.  Smith explains that he was distracted and did not mean it.  Yet, in this circumstance, given the dire consequences that can occur when someone is distracted while driving, this action (driving while distracted) is an injustice.  Therefore, Jones can go ahead with forgiveness even though there was no intent to harm.

In your mother’s case, she may not realize the depth of hurt she is causing you because of the Borderline Personality Disorder symptoms, but even so, a mother should not be treating her daughter with disrespect and in a consistently unjust way by stealing money repeatedly.  This is an injustice and so you can forgive your mother.  As a final point, the Borderline diagnosis suggests that your mother does have awareness at least to a degree of her actions (“borderline” means that she sometimes is rational and sometimes not) and so she may be aware at least at times of the impact of her actions on you.  If this is the case, then she may (at times) be intentional in her stealing behavior.  You should go ahead and forgive if you are ready.