Assalamualaikum ustaz. Is it permissible to bring Zamzam water out of Mecca to get its advantages when one returns home? Thank you.
Waalaikumussalam wrt. wbt.,
Alhamdulillah, praise and gratitude to Allah SWT for His countless blessings for us all. Praise and salutations to our beloved Prophet Muhammad PBUH, his family, companions, and all those who follow his footsteps until the Final day.
We start with the statement of Allah SWT:
رَّبَّنَا إِنِّي أَسْكَنتُ مِن ذُرِّيَّتِي بِوَادٍ غَيْرِ ذِي زَرْعٍ عِندَ بَيْتِكَ الْمُحَرَّمِ رَبَّنَا لِيُقِيمُوا الصَّلَاةَ فَاجْعَلْ أَفْئِدَةً مِّنَ النَّاسِ تَهْوِي إِلَيْهِمْ وَارْزُقْهُم مِّنَ الثَّمَرَاتِ لَعَلَّهُمْ يَشْكُرُونَ
“Our Lord, I have settled some of my descendants in an uncultivated valley near Your sacred House, our Lord, that they may establish prayer. So, make hearts among the people incline toward them and provide for them from the fruits that they might be grateful.” 
Zamzam water is the best water of all in this world. Zamzam is the name of a water spring in Masjidil Haram in Mecca. The emergence of this water spring dates back to the time of Prophet Ismail and Ibrahim AS when Allah SWT specifically granted for Prophet Ismail and his mother when the water they brought was finished in the barren Mecca at the time.
Among the special characteristics of Zamzam water is that it is blessed water and can satiate hunger. This is as stated in a hadith from Abu Zar RA, where the Prophet PBUH said:
إِنَّهَا مُبَارَكَةٌ إِنَّهَا طَعَامُ طُعْمٍ
“Indeed, Zamzam water is filled with blessing and contains fulfilling food.” 
Furthermore, Zamzam water is the best of water on this earth and the cure of diseases. There is a narration from Abdullah bin Abbas, the Prophet PBUH said:
خَيْرُ مَاءٍ عَلَى وَجْهِ الْأَرْضِ مَاءُ زَمْزَمَ فِيهِ طَعَامٌ مِنَ الطُّعْمِ وَشِفَاءٌ مِنَ السُّقْمِ
“The best of water on this earth is Zamzam water and it contains fulfilling food and the cure of diseases.” 
Moreover, al-Munawi stated that Zamzam water is the best of all water, the most honoured of water, valuable and favoured by people. It is dug by the angel Gabriel and the water is given to Prophet Ismail AS. 
Hence, it is undeniable that the Zamzam water has special blessings and advantages such as satiating and a cure for all diseases. Furthermore, it is also the best water that can be found on earth as well as blessed.
Moreover, Ibn Qayyim al-Jauziyyah also narrated his own experience with Zamzam water saying:
“Indeed, I and others have experienced amazing results when using Zamzam water for treatment. I was cured of several illnesses that I experienced by the will of Allah. Furthermore, I’ve witnessed a person who made Zamzam water as his food for days, for around half a month or more and he never felt hungry. Concurrently, he performed tawaf the same way as others do. He told me that sometimes he’ll be like that for forty days and he’s the strength to be with his wife (intercourse), fast and perform tawaf numerous times.” 
Likewise, the blessings and advantages of Zamzam water aren’t bound with the honor of the Holy land. We’ve discussed this matter in-depth in our article titled: #369 The Blessings of ZamZam Water Isn’t Bound to the Holy Land. 
The permissibility of bringing Zamzam water out
Regarding this matter, Dr Nasir bin ‘Abd al-Rahman has stated in his book that scholars have agreed on the permissibility of bringing zamzam water to any state for the purpose of tabarruk – taking the blessing – from it.  This is based on a hadith from Aisyah R.Anha where she said that she brought Zamzam water out of Mecca and narrated:
أَنَّ رَسُولَ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ كَانَ يَحْمِلُهُ
“Rasullullah PBUH once brough Zamzam water (for a journey).” 
Abu al-‘Abbas al-Sawi also stated in his hasyiah that it is sunnah to bring Zamzam water out and its advantages remain – it isn’t lost – different from those who claimed that its advantages are lost – when it is transported out of Mecca. 
While Syeikh al-Islam Ibn Taimiyyah said that it is permissible to bring Zamzam water out on a journey, for previous scholars would usually bring it with them. 
Furthermore, Ibn Hajar al-Haitami also said that Zamzam water is transported to his country for medicinal purposes and taking the blessing from the Zamzam water for himself or others. 
According to the above discussions and arguments, in our opinion, it is permissible to transport Zamzam water out of Mecca for medicinal purposes, taking the blessing or other advantages or others, whether it is for himself or others. Moreover, there are scholars who ruled it sunnah and encouraged it.
May Allah SWT grant us all a clear understanding in religion. Amin.
 Surah Ibrahim: 37
 Narrated by Muslim (2473)
 Narrated by al-Fakihi in Akhbar Makkah (1106); al-Tabarani (11167); al-Dhiya’ in al-Ahadith al-Mukhtarah (137); Also see Majma‘ al-Zawaid wa Manba‘ al-Fawaid, 3/286; Silsilah al-Ahadith al-Sahihah, 3/44-45; its narrators are thiqah and Ibn Hibban stated that it is sahih.
 See Faid al-Qadir Syarh al-Jami‘ al-Saghir, 5/404.
 See Zad al-Ma‘ad fi Hadyi Khair al-‘Ibad, 361/4.
 See al-Tabarruk, (Pub. Maktabah al-Rusyd), pg. 293.
 Narrated by al-Tirmizi (963)
 See Hasyiah al-Sawi ‘ala al-Syarh al-Soghir, 2/44.
 See Majmu‘ al-Fatawa, 26/154.
 See Tuhfah al-Muhtaj, 4/144.