Praise be to Allah, and may blessings and peace be upon the Messenger of Allah. To proceed:
It has been authentically established in the hadiths that whoever drinks from the Hawd of the Prophet ﷺ on the Day of Judgment will never thirst thereafter. He ﷺ said:
“My Hawd is a journey of one month. Its water is whiter than milk, its fragrance is more pleasant than musk, and its vessels are like the stars of the sky. Whoever drinks from it will never thirst again.” Narrated by al-Bukhari and Muslim.
It is also authentically reported that he ﷺ said:
“I will be waiting for you at the Hawd. Whoever reaches it will drink from it, and whoever drinks from it will never thirst thereafter.” Narrated by al-Bukhari and Muslim.
These hadiths include both men and women; whoever drinks from the Hawd will never thirst thereafter.
There is also evidence indicating that the Prophet ﷺ would hand some members of his Ummah vessels from the Hawd. He ﷺ said:
“Then, when I leaned forward to give them some, they were pulled away from me.” Narrated by al-Bukhari. The apparent meaning of the hadith is that he ﷺ intended to give them drink himself.
Therefore, there is nothing wrong with a woman or a man asking Allah to give them a pleasant drink from the hand of the Prophet ﷺ, after which they will never thirst again.
The fact that a woman is unrelated to the Prophet ﷺ does not prevent this, because matters concerning the Hereafter in this regard cannot be compared to the rules governing interactions between men and women in this worldly life. Scholars have also mentioned that the Prophet ﷺ had certain special privileges in this world that do not apply to others.
And Allah تعالى knows best.