Here's an excerpt and reference if you want more background for the question:
"Obviously, the fealty of the person who agrees to be the elect of a valid Conclave must be presumed a priori. However, Leo XIII expressly declared (“Apostolicae Curae”, September 13, 1896; D.S. 3318): “The Church must judge intention in the way it is exteriorly manifested”. Did the “occupant” (of the Apostolic See), accepting the election of the Conclave, really have the intention to receive the Communication exercised by Christ? To answer this question we must, according to Leo XIII, consider the FACTS. If the “occupant” had, in reality, the intention to receive the above-mentioned Communication, then he should have AFTERWARDS, and HABITUALLY con-formed himself to all the exigencies of said Communication. If, on the contrary, it is ascertained that the “occupant” CONTINUOUSLY AND SYSTEMATICALLY acts against the most fundamental exigencies that are inherent to the Communication exercised by Christ, WE MUST CONCLUDE, (according to Leo XIII) that the “occupant” did not have, in reality, the intention to receive it, and that, in consequence, he never was [or he ceased to be] the Pope FORMALITER."
https://www.sodalitiumpianum.com/interview-bishop-guerard/
While I'm waiting for you to reply to my last post, I will comment on the errors in the quote above that you provided.
Leo III was referring to the intention that is required for a minister to validly confer a sacrament. Receiving the papal is not a sacrament. Hence, this is apples and oranges.
It is true that the man elected must have the intention of accepting the office that he was elected to fill. This inention is manisted externally during the council by his acceptance. Francis evidently manifested this intention by accepting the election or he would not have been presented to the world as the Pope by the Protodeacon.
The quote you provided says the person must manifest the intention "to receive he communication exercised bu Christ" (bu which he must mean jurisdiction, which the newly elected Pope receives from Christ) by "AFTEERWARDS and HABITUALLY confrming himself to all said Communications." In other words, he must be
impeccable in exercizing the office of Pope.
Sorry, but this is erroneous reasoning, to say the least.
The newly elected Pope manifests his intention to receive the papacy when he says "I accept" during the conclave. If, as the confused author you quoted believes, a man who is validly elected pope by a conclave must manifest his intention to receive the office "by habitually conforming himself to all said Communications," ther would be no way of knowing if he is a true pope until he dies, since prior to that, he could aways fail "to conform himself to all said Communications," and thereby manifest that he never had the requisite intenton to accept the office.