The flat can be trasnferred to your name by your sister by way of a gift deed and the same would attract 2% stamp duty as per the provisions of the Bombay Stamp Act and a further 1% charge towards registration fees or Rs. 30,000/- whichever is lower on that account.
Yes, you can give a POA to your mother to conclude the sale on your behalf. The POA can be executed by you before the Indian Embassy in Tanzania or closest to you and the same can then be forwarded to India for adjudication and payment of stamp duty and thereupon your mother can utilise the same for concluding the sale.