Yes, this scapular has been approved by the Church. It was approved by Pope Pius IX in 1863 and again in 1870.

However, the Apostolate of the Green Scapular that you mention claims that a woman named Anna Marie, who is a founding member of the Apostolate, is allegedly receiving messages from God the Father. These messages are being promulgated through the website. It should be understood that these messages are not Church approved.

It is also not necessary to write the person's name on the scapular. God already knows who it is!

The green scapular came about as the result of an apparition of Our Lady in 1840 to Sister Justine Bisqueyburu, a Daughter of Charity of St. Vincent de Paul - the same order as St. Catherine Laboure who received the Miraculous Medal just 10 years earlier. The green scapular bears an image of the Immaculate Heart of Mary on one side. The other side contains an image of the Immaculate Heart pierced by a sword and surrounded by the inscription, "Immaculate Heart of Mary, pray for us now and at the hour of our death."

Promulgation of the scapular was delayed due to skepticism from Sister Justine's superiors and the Church, but was eventually approved by the local bishop. During this time, Our Lady appeared again on September 8, 1846, to clarify how the scapular was to be used. No enrollment was necessary, and it need only be blessed by a priest and worn by the person who wishes to benefit from Our Lady's intercession. Only one daily prayer is required, the same as the words inscribed on the scapular: "Immaculate Heart of Mary, pray for us now and at the hour of our death."

Perhaps the most unique and best-known quality of the green scapular is the fact that it can be hidden in the belongings of someone who refuses to wear it, and the prayer said for that person. Even though the most powerful graces are reserved for those who wear it with devotion, graces in proportion to the confidence of the person praying can be awarded to someone among whose possessions the scapular is hidden.

The Society of the Green Scapular in Front Royal, Virginia reports numerous miracles attributed to the faithful wearing of this scapular, including physical and spiritual healings.

"Family and friends, who had fallen away from the Catholic Faith, and even those who never had faith, came to embrace the Sacraments (sometimes after being away a lifetime)," the Society reports. "People involved in dangerous relationships saw their bad companions change for the better or leave the relationship. Work environments witnessed an increase of purity in speech, modesty in dress and charity in behavior."

As is the case with all scapulars, they are sacramentals which were instituted by the Church to be "sacred signs which bear a resemblance to the sacraments. They signify effects, particularly of a spiritual nature, which are obtained through the intercession of the Church. By them men are disposed to receive the chief effect of the sacraments, and various occasions in life are rendered holy" (Catechism No. 1667)

As such, they "do not confer the grace of the Holy Spirit in the way that the sacraments do, but by the Church's prayer, they prepare us to receive grace and dispose us to cooperate with it" (No. 1670).

In other words, a scapular, medal, set of rosary beads, holy water, etc. are not "lucky charms" that have some kind of power. Their power lies in the faith they represent. As SN states above, "the scapular is only as powerful as the user believes it will work."

This is true, which is why Jesus taught that if we have faith the size of mustard seed, we really can move mountains! (Matt: 17:20)