A Flemish, Dutch-speaking professor of chemistry, Dr. Mark Waterinckx from Bruges, Belgium, who was formerly himself involved in promoting both Medjugorje and San Damiano, has presented proof, that both apparitions, even though separate, are not authentic and either the product of grotesque forgery (Medjugorje) or of human imagination (San Damiano).
I don't know much about Mama Rosa, the San Damiano supposed, seer, though. She seemed pious and wore a thick veil at all Masses though, at the photographs I have seen so far.
But no, it is not authentic.
Please note, that e.g. the Society of Saint Pius X, except in case of the approved Fatima, Lourdes, Knock, Banneux and La Salette apparitions, is very critical about "apparitions" and mystical claims. Abp. Lefebvre more than once warned his faithful about all these supposed messages. He thereby clearly expressed the counsel St. John of the Cross, himself a mystic, gave to the Church. Shun all such mystical claims, presume they are not authentic until proof. (One exception in the SSPX is His Excellency Bishop Richard Williamson, who firmly believes in the authenticity of the Garabandal apparitions and prophecies.)
A wise position.
We have seen so many tragical incidents with fraudulent apparitions and claims to be the "sole true remnant of the Church' and the "divinely willed reform movement". All pious people, but still in grave error. Look at the claims by Sr. Feliksa Koz³owska who claimed she was an elect, received direct messages from Our Lady and was supposed to found a true reform movement of priests etc. When her apparitions and the suggested religious congregation were finally rejected by Pope St. Pius X in 1906, even though the saintly Pontiff had been quite positive towards the piety of the priests and the seer/messenger, they founded their own Old Catholic schismatical ecclesial body (see Mariavite Old Catholic Church). There is the supposed mystical La Salette "pope" sect of Fr. Michel Colin OCJ, who declared himself pope, a mystically "consecrated" "bishop" and "leader of the true church" (which nevertheless ordains women, but is a cult in isolation). There is the famous case of the Palmar de Troya apparitions to a couple of young children in the late 1960s, deemed authentic initially by many good Roman Catholics. When around 1974 a new seer of the group Clement Domínguez y Gomez wanted to found a religious congregation (Carmelite Order of the Holy Face) he quickly received support (already many scores of otherwise good, traditional, and pious elderly and younger Roman Catholic diocesan priests and monastic priests from religious Orders had joined him or supported them with sacramental service) and even found Abp. Ngo Dinh Thuc, who believed the apparitions, to conduct at first priestly ordinations and finally five episcopal consecrations. Without an apostolic Mandate of course, for Paul VI ("The Martyr Pope") was supposedly held imprisoned by cardinals in the Vatican. But after 1976 Dominguez increasingly made "prophecies" that he would succeed Paul VI. Thuc cut off all contact with the Palmar de Troya group and was absolved by Paul VI himself. In 1978 Spanish Palmar de Troya became the "see" of the Palmarian "Catholic" and "Holy" Church of the End Times. They seemingly were "traditionalist", but they quickly reformed, engaged in homosexuality, ordained young boys, revised the liturgy of their Mass entirely and made all kinds of nonsense.
In the popular fraudulent apparitions' village of Medjugorje the local Franciscan priests supporting the supposed "seers" for more than 25 years, were so rebellious, that after the local diocesan Croatian bishop had rejected the apparitions, they invited a German (schismatic and liberal) Old Catholic bishop to perform Confirmations in their supposedly Roman Catholic parish. The "apparition" approved all of this. The pattern is very clear. Fraudulent apparitions > rebellious behaviour > illegal Holy Orders and sacraments > foundation of a schismatical and heretical ecclesial body supposed to be a or thé "true Church". Stay away from false apparitions. The Roman Church will approve if God wants it. And if not, even if they were authentic, nobody is bound to apparitions, nor is anyone obliged to accept them, and they do not form a necessary thing for eternal salvation.
We mayhowever trust in the authentic officially approved apparitions and we should of course venerate them, as they have received the constant approval of the Holy See, which is the norm for all things as to faith and discipline.