Can I transfer property from my mother to myself?

1) If your sister has a POA, she has the legal authority to do this. You can do it before your mother passes (so before probate), the same as your mother could transfer it if she were mentally competent and wanted to. (The POA gives your sister the same authority as your mother has over her property.)
2) Be aware that getting a house is like getting an amount of money equal to the cash value of the house: there will be a tax consequence. Since this is the equivalent of getting a gift, your mother will have a large gift tax bill--and if it can't be paid, there are situations where the IRS could go after the house or, if it was already sold to some 3rd party, you and/or your sister. (You can't help people avoid taxes or hide assets from the IRS.)
3) If your mother has received or will received Medicaid (e.g. the state is paying for her nursing home or medical treatment), then the state can go after the home and take it, notwithstanding that it was transferred to you, or, if it was already sold to a 3rd party, go after the money received for the home. (You can't hide a person's assets from Medicaid, and Medicaid can seek reimbursement of what they paid for someone's care from any assets transferred by them for less than fair market value within the last 5 years.)
In short, there are some issues to be considered before doing this (though again, you *can* do this) and you may wish to consult with an accountant or CPA before deciding what to do.