According to the American Bar Association, agents for grantors should sign legal documents one of two ways. Either "Mother, by Daughter under POA". Or, "Daughter, attorney-in-fact for Mother".
It would also be a good idea that the person actually present the POA as proof it exists. For more information on the ABA's position on POA agreements, click the link below:
Now, whether the lease agreement is void or voidable would be a question of fact. Whether the lease is void from inception will depend on whether the daughter actually had a valid power of attorney to enter into the lease. If the daughter did have POA, then arguably, the signature is still improper in its present form. But then, one would be compelled to ask the question: are you trying to get out of a lease using a technicality not previously challenged? You would be hard pressed to argue that a lease should be cancelled if you have lived somewhere for awhile and are only now challenging what may be an improper signature.
DISCLAIMER: Brandy A. Peeples is licensed to practice law in the State of Maryland. This answer is being provided for informational purposes only and the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship. For legal advice relating to your specific situation, I strongly urge you to consult with an attorney in your area. NO COMMUNICATIONS WITH ME ARE TO BE CONSTRUED AS ARISING FROM AN ATTORNEY-CLIENT RELATIONSHIP AND NO ATTORNEY-CLIENT RELATIONSHIP WILL BE ESTABLISHED WITH ME UNLESS I HAVE EXPRESSLY AGREED TO UNDERTAKE YOUR REPRESENTATION, WHICH INCLUDES THE EXECUTION OF A WRITTEN AGREEMENT OF RETAINER.
I concur with Attorney Peeples' fine response.
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I do not think the lease would be declared void under the circumstances you presented.
I think "she" would be liable either personally or as a POA even she she did not sign
The answer given does not imply that an attorney-client relationship has been established and your best course of action is to have legal representation in this matter.