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If the person has transferred their life estate to you then if they are still in possession of the property by storing their personal property there, then they are legally a tenant and then you have a couple options....one completely safe but longer, and the other quicker but a little riskier.
The safest one is to just post a written 30 day notice to terminate their tenancy (I realize that they are in TX and won't ever see it, legally that isn't relevant) and then you evict them formally through the courts to get a judgment of eviction and a writ of possession that the sheriff will execute and then deliver legal possession to you. You can then just dispose of any personal property that was left there.
The other option is to send her a written notice certified and first class mail stating that you are terminating her "bailment" (which is when one party leaves personal property in the possession of someone else) and she has XX days to come get it or you will consider it abandoned and dispose of it. You decide what XX is, but it must be reasonable....maybe 10 days. Then if they don't come get their stuff, you can dispose of it however you want. If they then tried to sue you, you have proof via the certified mail receipt that you notified them and gave them an opportunity to reclaim the property before it was disposed of.