Where did you hear that? I don’t believe you got your story straight.

According to popular tradition, a merchant acquired the icon of Our Lady of Perpetual Help from the island of Crete and had it shipped to Rome towards the end of the fifteenth century.  During the voyage, a terrible storm arose, threatening the lives of all on ship.  The passengers and crew prayed to our Blessed Mother, and were saved.
Once in Rome, the merchant, dying, ordered that the image should be displayed for public veneration.  His friend, who retained the image, received further instructions: in a dream to his little daughter, the Blessed Mother appeared and expressed the desire for the image to be venerated in a Church between the Basilicas of St. Mary Major and St. John Lateran in Rome.  The image, consequently, was housed at the Church of St. Matthew, and became known as “The Madonna of Saint Matthew.”  Pilgrims flocked to the church for the next three hundred years, and great graces were bestowed upon the faithful.
After Napoleon’s troops destroyed the Church of St. Matthew in 1812, the image was transferred to the Church of St. Mary in Posterula, and remained there for nearly forty years.  There, the image was neglected and forgotten.
By divine providence, the forgotten image was rediscovered.  In 1866, Blessed Pope Pius IX entrusted the image to the Redemptorists, who had just built the Church of St. Alphonsus, down the street from St. Mary Major.  As a boy, the Holy Father had prayed before the image in the Church of St. Matthew.  He ordered the public display and veneration of the image, and fixed the feast of Our Lady of Perpetual Help as the Sunday before the Feast of the Nativity of St. John the Baptist.  In 1867, when the image was being carried in a solemn procession through the streets, a young child was cured, the first of many recorded miracles attributed to Our Lady of Perpetual Help.
To this day, the Church of St. Alphonsus displays the icon of Our Lady of Perpetual Help and welcome pilgrims for prayer.  May each of us never hesitate to invoke the prayers and intercession of Our Blessed Mother in time of need.


https://catholicstraightanswers.com/what-is-the-story-behind-the-image-of-our-lady-of-perpetual-help/

olor=rgba(0, 0, 0, 0.921569)]“In 1918 during the Spanish Influenza epidemic the pastor of St Peter’s church in Philadelphia, which has the Shrine of St John Neumann, asked Our Lady of Perpetual Help to spare the parishioners from the flu.  St Peter’s was one of the few churches that was able to remain open during the epidemic and no parishioners died of the flu.  Let us, then, invoke Our Lady of Perpetual Help’s intercession during this epidemic.[/color]


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For me, there is no more beautiful image of the Blessed Virgin that of Our Lady of Perpetual Succour. As a child in our parish church on a Wednesday night there would be the Perpetual Novena to Our Lady under this title, very well attended. 

My mother had this image prominently displayed in more than one room and I now possess one of those. 

The link you provided, Viva, has wonderful history but the picture is disappointin because it does not illustrate all the beautiful meaning in the original.

Such as

https://www.saintsfeastfamily.com/copy-of-st-cyril-of-alexandria-june

[color=rgb(var(--color_15))]AN BRIEF EXPLANATION OF THE SYMBOLISM IN THE ICON OF OUR LADY OF PERPETUAL HELP
[color=rgb(var(--color_15))]Our Lady of Perpetual Help, also known as Our Lady of Perpetual Succour, is a title given to the Blessed Virgin Mary by Pope Pius IX, associated with a celebrated Byzantine icon of the same name dating from the 15th century. This icon has been in Rome since 1499, and is currently in the church of Sant’Alfonso di Liguori all’Esquilino. The image has become very popular among Roman Catholics in particular, and has been very much copied and reproduced.

(1)  Meaning of Our Lady of Perpetual Help Icon1) Greek initial for Mother of God.
(2)  Greek initial for St. Michael, the archangel.
(3)  Greek initial for St. Gabriel, the archangel.
(4)  Mary’s mouth is small for silent recollection. She speaks little.[/color]
[color=rgb(var(--color_15))](5)  Mary’s eyes are larger, for in all our troubles, they are turned towards us always.[/color]
[color=rgb(var(--color_15))](6)  Star on our Lady’s veil means she is the star of the sea who brought the light Jesus into this world.
(7)  Red tunic is the color worn by virgins at the time of Christ (AD33).
(8)  Christ’s hands turned palms down into his mother’s indicate that the grace of redemption is in her keeping.
(9)  Mary’s left hand supports Christ possessively. That means she is his mother. It’s a comforting hand for everyone who calls on her.
(10)  Dark blue mantle – the color worn by mothers in Palestine. means Mary is both virgin and mother of Christ.
(11)  The entire background is gold representing the heaven.[/color]
[color=rgb(var(--color_15))] [/color]
[color=rgb(var(--color_15))]Our Lady of Perpetual Help[/color]
[color=rgb(var(--color_15))](12)  Golden crown placed on the original picture as a token of many miracles wrought by our lady invoked under the title of perpetual help.
(13)  Greek initials for Jesus Christ.
(14)  Foot with falling sandal represents Christ’s divine nature, barely clinging to earth. The human nature is symbolized in the other foot to which the sandal is more firmly bound. This simply means that Christ has two natures, Human and Divine.[/color][/font][/color]

I heard that the Icon of Our Lady of Perpetual Help was stolen from a Greek Orthodox monastery centuries before the image was publicly venerated. However I also heard a girl had a vision to place it a certain place and it wasn't the Greek Orthodox monastery it came from. This case makes me curious when God would regard a long stolen object as someone else's. Would the Shroud of Turin rightfully belong to Italy rather than Constantinople even though it was stolen there?

Perhaps you are thinking of the icon of Our Lady of Kazan of the Russian Orthodox?

According to tradition, the original icon of Our Lady of Kazan was brought to Russia from Constantinople in the 13th century. After the establishment of the Khanate of Kazan (c. 1438) the icon disappeared from the historical record for more than a century.
Metropolitan Hermogenes' chronicle, written at the request of Tsar Feodor in 1595, describes the recovery of the icon.^{[1][unreliable source?]} According to this account, after a fire destroyed Kazan in 1579, the Virgin appeared to a 10-year-old girl, Matrona, revealing the location where the icon lay hidden. The girl told the archbishop about the dream but she was not taken seriously. However, on 8 July 1579, after two repetitions of the dream, the girl and her mother recovered the icon on their own, buried under a destroyed house where it had been hidden to save it from the Tatars.