From www.medias-presse.info comes the following excerpt of a letter from Cardinal Müller to Bishop Bernard Fellay. According to www.medias-presse.info, Cardinal Müller's letter was communicated to all SSPX members by the SSPX General House.
Excerpt from Cardinal Müller's letter:
“As you know, Pope Francis has many a time manifested his benevolence towards your Priestly Society, granting, in particular, to all priest members the faculty of confessing the faithful validly and by authorizing local Ordinaries to grant licences for the celebration of the marriages of the faithful who follow the pastoral activity in your Society. Furthermore, discussions are continuing concerning questions relative to the full re-establishment of the communion of your Society with the Catholic Church.
In relation to this, with the approbation of the Sovereign Pontiff, I judged it necessary to submit to the Ordinary Session of our Congregation (which met on May 10 last) the text of the doctrinal Declaration which was transmitted to you during the meeting of June 13 2016, as the necessary condition in view of the full re-establishment of communion. Here are the unanimous decisions of all the members of our Dicastery in this regard:
1) It is necessary to require the adhesion of the members of the Priestly Society of Saint Pius X to the new formula of the Professio Fidei dating from 1988 (c.f. annexe). Consequently, it is not sufficient to ask them to express the Professio Fidei of 1962.
2) The new text of the doctrinal Declaration must contain a paragraph in which the signatories declare in an explicit manner their acceptance of the teachings of the Second Vatican Council and those of the post-conciliar period, by granting to said doctrinal affirmations the degree of adhesion which is due to them.
3) The members of the Priestly Society of Saint Pius X must recognize not only the validity, but also the legitimacy of the Rite of the Holy Mass and of the Sacraments, according to the liturgical books promulgated after the Second Vatican Council.”
www.medias-presse.info adds that Cardinal Müller concluded the letter saying that “during the Audience granted to the Cardinal Prefect on May 20 2017, the Sovereign Pontiff approved these decisions”. The French website also adds that in his accompanying letter to SSPX priests, Father Christian Thouvenot, Secretary General of the SSPX, recalled the words of Bishop Fellay after the meeting of the major superiors in Anzère, Switzerland, on June 28 2016:
“The Society of Saint Pius X does not seek primarily a canonical recognition, to which it has a right because it is Catholic. The solution is not simply juridical. It pertains to a doctrinal position which it is imperative to manifest [...] Divine Providence will not abandon Its Church whose head is the Pope, Vicar of Jesus Christ. That is why an incontestable sign of this restoration will reside in the signified will of the Sovereign Pontiff to grant the means for re-establishing the order of the Priesthood, the Faith and Tradition – a sign which will be, furthermore, the guarantor of the necessary unity of the family of Tradition”.