Is it permissible to give a portion of Zakat funds received from abroad to a needy female relative for essential surgeries?

What you did by distributing this money is permissible, and you will be rewarded for it. This woman, in the described state of need, poverty, and inability to afford treatment, falls within the categories of those eligible to receive zakat. Your zakat, and the zakat of those who authorized you to disburse theirs, has been properly discharged and fulfills the obligation.