It can't be done at all. Your sister can resign her POA, of course; but she can't pass it on to you.
Only your mother can give power of attorney to someone. I get that your mother has dementia, but how is her mental functioning so far? If she is still technically, legally "competent" - i.e. capable of understanding what a POA is, and what she is doing if she gives this authority to you - then she can create a new POA.
If she is no longer able to do that, then your sister can continue as POA except that you will be acting for her 'on the ground', so to speak. Note, I wouldn't necessarily recommend that because it can get fraught and it can get complicated; but it depends on how well you and sister work as a team.
Alternatively, if there is a good deal to be done on your mother's behalf and she's no longer able to grant POA, you may have to consider guardianship. But you can do quite a lot for your mother purely as her next of kin. Do you think not having a POA on site will necessarily be a problem?
Nope! Your mother gave it to your sister and only she can change it to you. If your mother's dementia is not very advanced that she is still considered competent, then she can see a lawyer and have one written up. Are you sure that the current document does not list you are a secondary POA in case your sister can't do it?
Only your mother can give power of attorney to someone. I get that your mother has dementia, but how is her mental functioning so far? If she is still technically, legally "competent" - i.e. capable of understanding what a POA is, and what she is doing if she gives this authority to you - then she can create a new POA.
If she is no longer able to do that, then your sister can continue as POA except that you will be acting for her 'on the ground', so to speak. Note, I wouldn't necessarily recommend that because it can get fraught and it can get complicated; but it depends on how well you and sister work as a team.
Alternatively, if there is a good deal to be done on your mother's behalf and she's no longer able to grant POA, you may have to consider guardianship. But you can do quite a lot for your mother purely as her next of kin. Do you think not having a POA on site will necessarily be a problem?