Since the Papacy claims so-called "apostolic succession" from the Apostle Peter--( a dubious claim) can anyone picture Peter writing such a Letter?--OF COURSE NOT....
Peter's Counsel: Dearly beloved, I beseech you as strangers and pilgrims, abstain from fleshly lusts, which war against the soul;
1 Peter 2:11
Pope's Counsel: "Pope Francis has written a third supportive
letter 
to LGBTQQIAAP2S+ advocate Father James Martin, promising prayers
for the success of a Pride conference to be held in New York this month.
“I send my best regards to the members of the meeting at Fordham University,” the pontiff wrote to his fellow Jesuit. “You and all who are working at the Outreach Conference are in my prayers and good wishes.”
As he has done on other occasions, the pope praised Father Martin for “all the good you are doing.”
“Thank you, thank you for your witness,” he added.
The pope’s handwritten letter is dated May 6, 2023,
and refers specifically to the Outreach LGBTQ Catholic Ministry
Conference to be held at Fordham University from June 16 to 18. 
Last year, Father Martin declared that churches have a special duty to celebrate Gay Pride since much anti-gay violence has been “motivated by religion.” Catholics should celebrate Pride Month he said.
While enjoying special protection from Pope Francis, Father Martin has come under fire from other Catholic prelates for affirming people in their immoral sexual behavior rather than calling them to repentance and conversion."
Breitbart