Without the power of attorney of the property owner, legally speaking, the owner's mother has no right to sign the lease contract on behalf of the owner.

Of course, there are two ways to legalize the unauthorized agency contract. One is ratification, that is, the owner of the house ratifies the agency behavior of the unauthorized agent.

The second is to see if it constitutes an apparent agency. Apparent agency refers to the agency behavior with a bona fide third party, which bears legal consequences. Although the actor has no agency right, his own behavior has caused enough appearance to convince the bona fide third party that he has the agency right.

General jurisprudence holds that the mother's identity cannot constitute the condition of agency by estoppel. If her mother shows the power of attorney signed by her son (whether true or false), the third party has enough trust conditions based on her mother's identity and the fact that the real signature cannot be verified in practice, thus constituting the elements of agency by estoppel.

Therefore, I suggest that you ask the other mother to issue a power of attorney signed by her son. Whether it is really the signature of the other son or not, as long as the third person (you) can get enough trust from the other mother, then this behavior constitutes an agency by estoppel, even if it does not constitute an authorized agent, so that you can legally lease the property.