Ah, yes, the Fatimskaya icon. I too love this icon.
The first time I saw the Fatimskaya was in a special issue of SOUL magazine. It shows the late founder of the Blue Army, Monsigner Harold Colgan, holding it in his hands. (I have the image as a JPEG, but am unable to upload it to this post)
The first time I saw the Fatimskaya icon in person was during my first visit to Our Lady of Fatima Russian Byzantine Catholic Church in San Fransicso in 1995. At the time, the parish bookstore did sell holy card versions of the icon, however, I didn't see anymore of them at my last visit three years ago.
As to the origins of the Fatimskaya icon, here is what I have collected from personal research:
"The titilar eikon of the center, Our Lady of Fatima, is a contemporary work, executed in Paris according to the classic canons of Russian eikon painting, that is to say, applying egg tempura to a carefully prepared wood surface. Our Lady appearing to the three children in the elongated hieratic form associated with high Russian iconographic art." - The Russian Catholic Center in San Francisco, California, Eastern Churches Quarterly
So, according to the article, the icon was written in Paris according to the traditional manner.
Here is more info about the icon from the booklet, Welcome to the Byzantine-Russian Catholic Chapel in Fatima
, written by the late Mitred Archimandrite John Mowatt, former rector of the Byzantine Chapel at Fatima:
"This particualr icon is of an ancient Russian source and in copying the icon the artist just added the figures of the three Seers, Lucia, Francisco, and Jacinta. It is interesting to note here that the Russian Church already had an icon of the Most Holy Virgin Mary, clothed in white, and appearing on top of a tree as she radiated and drew the peoples of the world towards her. This is more than just a mere coincidence as, generally speaking, most Russian and other Byzantine icons of Our Lady always portray her as holding the Divine Child."
According to this article, another icon served as the basis for the Fatimskaya. From my research, that "ancient icon" of the Theotokos appearing in white above a tree was a variant of the "Joy of All Who Sorrow" icon.
Below is a version of the "Joy of All Who Sorrow" Icon".
Notice the position of Christ above Mary. He is depicted much like on the Fatimskaya. Also, notice the similarities of the people on both sides of the Theotokos. Again, much like the Fatimskaya.
Unfortunately, there is no mention of who the iconographer was, and Archminadrite John passed away before I could contact about it.
I hope this helps.