Yes, you can file a tax return for your mother as her Power of Attorney (POA).
When filing her return in TurboTax, prepare the return as usual with her information. When prompted about who prepared the return, indicate that you prepared it as her authorized representative. In the signature section, sign your name followed by "POA". Keep a copy of the POA with your records.
It's also a good idea to get a signed Form 2848 so that the IRS can discuss her return with you.
This may be helpful
If you are using desktop, you can prepare and file up to 5 different returns.
Mechanically, to file the return, you will need SSN and specific driver's license number, the prior year's returns AGI (for security) and bank or credit card numbers for payment or refund.
This is how I did my parent's return. Now can you/should you not somewhere in the software that you are filing as their POA instead of them? Perhaps. I don't know how to do that. The 1040 form has a line for prepared by. I don't know how to fill that in with Turbo tax.
This says turbo tax only accommodates self prepared, so you woul d have to do it as described above, I assume