One principle of genealogy is that you should start with things you know and move backwards to things you do not yet know. I assume you have information going back from yourself to your parent, grandparent, and finally your great-grandfather named Fakun.
According to https://en.m.wikipedia.org/wiki/Mauritians_of_Indian_origin and similar sources, much of the population of Mauritius descends from workers who came from India, especially Bihar, as indentured servants to work on plantations after slavery was outlawed. So your belief that Fakun was from Bihar is certainly reasonable.
As to your mention of the ship Sultany arriving in Mauritius in 1847, it is recorded as you say in a report to a British committee here: https://books.google.com/books?id=aHZbAAAAQAAJ&pg=PA329&lpg=PA329&dq=sultany+mauritius+1847&source=bl&ots=f3FJZhpCdP&sig=oAX9OE1P5QbEnd3aaTEOcZp8mrw&hl=en&sa=X&ved=2ahUKEwiq972uw9DeAhWDneAKHZeSA80Q6AEwAnoECAIQAQ#v=onepage&q=sultany%20mauritius%201847&f=false
I assume you know Fakun died in 1888 based on either a written document or from a story passed down through your family.
Following the principle of going back from the known to the unknown, the ideal way to find Fakun's place of birth in Bihar would be to find a record in Mauritius which lists his place of birth, and then find records from that place confirming his birth or residence in that place. A death record would help solve that, if one is available. The National Archives of Mauritius has a web site listing its holdings and contact information: http://nationalarchives.govmu.org/NationalArchivesServices/aboutus.do
The government of Mauritius also has a Civil Status Division which may have relevant information: http://csd.pmo.govmu.org/English/Pages/default.aspx
This page may also have helpful links: https://www.familysearch.org/wiki/en/Mauritius_Civil_Registration
Good luck with your research!
(If you update your question with more details, I may be able to make my answer more specific,)