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Keep the dates in mind. June 29, 2026, the Pope sent an urgent letter to the SSPX.
Then this reply letter was sent June 30.
July 1, 2026 - Historic Consecrations of four priests to the episcopacy in Écône, attended by approx. 20K
https://fsspx.news/fr/news/lettre-du-superieur-general-reponse-sa-saintete-le-pape-leon-xiv-59914

AI Translation: non-official please!!
Excerpt:
From Dossier  Sacres [French] website,

The Superior General
To His Holiness Pope Leo XIV

Écone, 30 June 2026

Very Holy Father,

  Be very much thanked for the letter You kindly addressed.

  I was deeply touched by Your fatherly solicitude.

  For a long time, I would have liked to have had the opportunity to meet with You in order to personally express our sincere desire to serve the Church. Unfortunately, this opportunity did not present itself.

  I just ask You to consider the authenticity of this intention, which is not fake. Paradoxically, in the current context, it seems to us precisely our duty to do everything possible to sew the tunic of Christ, torn apart by forces and pressures incompatible with an authentically Catholic spirit. I simply ask You to consider the authenticity of this intention, before making a decision concerning the Society of St. Pius X. It's not too late.

  Far from us the idea of separating ourselves from the Roman Church; on the contrary, we wish to serve it by extraordinary means - we come as to the aid of a mother in difficulty who needs a particular help, even if it is not understood by all. But I am sure that the Holy Father could understand this.

  The Holy See has already shown that it can understand very complex situations and take the necessary time.

  I would therefore allow myself to ask You filially to take the time required for this discernment.

  If my words were not enough, I would ask You to think about two very simple facts.

  First of all, the Society was already declared schismatic in 1988, for reasons and under circuмstances absolutely analogous to those of today; and yet, after so many years, we speak like a father with his son. Your Holiness paternally exhorts me to avoid a schism which, theoretically, would have already taken place. Do You not think that this very attitude, of which I deeply appreciate its solicitude, is precisely proof that the Society is neither schismatic nor hostile to the Church?

  Secondly,(...) the Holy See entrusted two bishops of the Church with the mission of dialogue with the Priestly Fraternity of St. Pius X: Bishop Vitus Huonder, then Bishop of Chur, now deceased, and Bishop Athanasius Schneider, (...) of Astana. Both, after taking the time necessary for discernment, recognized the profoundly Catholic spirit of the Society and publicly testified to it.

  But above all, I allow myself to address Your Holiness in the name of the thousands of souls who have found the Catholic faith and religious practice through the apostolate of the Society. This is a fact that Your predecessors themselves have taken note of. These souls have only one desire: to achieve salvation through this instrument which Providence has made available to them. They have suffered and they are sincere. I am certain that Your paternal heart of a universal Shepherd will be sensitive to this particular situation. One day, all the difficulties between the Holy See and the Society will be resolved. A gesture of understanding on Your part, far from harming unity, could only manifest in the eyes of the world and all Christians Your concern for unity and Your goodness of Father.

    I leave all this to Your benevolent consideration. I renew my prayer for Your Holiness.

  For a long time, even before Your election, I pray to Saint Rita for the present situation. I saw in the election of an Augustinian Pope a sign of hope. I am certain that the Holy One will intercede. It is never too late.

  Please give us Your blessing.

And I take this opportunity to renew to You the expression of my very profound devotion in the Lord.

Don Davide Pagliarani

(Unofficial Translation)