How would everyone know that its fake? This is what has been posted in a few books that were printed outside Iran and they listed it as being provided by Khomenis older brother (pasandideh??) to this certain author that I can not recall the name.
I am not presenting it as being a 100% accurate and we know how guarded pictures of these clerics and family members are. But that is something that has been used.
Khomeini's grandfather, Seyed Ahmad, left
Lucknow (according to a statement of Khomeini's elder brother,
Seyed Morteza Pasandideh, his point of departure was Kashmir, not Lucknow) some time in the middle of the nineteenth century on pilgrimage to the tomb of Hazrat 'Ali in Najaf. While in Najaf, Seyed Ahmad met Yousef Khan, a prominent citizen of Khomein. Accepting his invitation, he decided to settle in Khomein to assume responsibility for the religious needs of its citizens and also took Yousef Khan's daughter in marriage.
Seyed Ahmad, by the time of death, the date of which is unknown, had two children: a daughter by the name of Sahiba, and
Seyed Moustafa Hindi, born in 1885, the father of Khomeini. Seyed Moustafa began his religious education in Esfahan and continued his advanced studies in Najaf and Samarra (this corresponded to a pattern of preliminary study in Iran followed by advanced study in the "Atabat", the shrine cities of Iraq; Ayatollah Khomeini was in fact the first religious leader of prominence whose formation took place entirely in Iran). After accomplishing his advanced studies he returned to Khomein, and then married with Hajar (mother of Rouhollah Khomeini).
http://www.iranchamber.com/history/rkhomeini/ayatollah_khomeini.php