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Text messages can be used as evidence that an oral agreement was created by the parties, and oral agreements are generally enforceable. Usually, you'd need texts from both people showing what they talked about, though, to show there was an agreement. However, California law provides that a lease that is for MORE than one year must be in writing to be enforceable. Cal. Civ. Code, Section 1091. A text message MAY NOT be used to establish that parties entered into a written lease - you also need a separate writing. Section 1624(d). When a lease is invalid because it needed to be in writing and wasn't, then the parties have a month-to-month tenancy.
Any lawyer can subpoena copies of the text messages from the cell phone company if you needed them.
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The relevant time period isn't how long she was actually there - it's how long you agreed she was there. An agreement that someone will live in a property for 13 months must be proven by a writing and text messages are not sufficient. A month to month agreement that happens to last 13 months is a valid oral lease that doesn't need to be in writing. In that scenario, text messages are fine to prove that she was renting from you.
There are as many reason for a tenant to refuse to move out as there are tenants in Los Angeles, and most of them have nothing to do with you. It could be as simple as not having the money, not having anywhere to go, liking your house - or even sheer laziness. Now she's just making up laws. You're not a dorm. She doesn't get to to stay as long as she wants because she's in school.
Again, whether you can change your mind depends on what the texts said. If you said, "Sure, you can stay here for 13 months," that's not valid. If you agreed to allow her to stay any time period that is less than a year, the texts are valid and you would not be able to change your mind, but you can evict her as soon as the time period is up if she hasn't left.