You can read the 1956 speech by Mirza Mahmud Ahmad entitled Khilafat-i Haqqa Islamia at this link.
Page 2, top lines: “though Pope and the Papal system has become corrupt, we must not let this make us think why is a resemblance being given with them [in khilafat verse of the Quran]”
Page 2: “Look at the Christians. Even if their khilafat is false, they have continued it for 1900 years. But the misfortune of the Muslims is that the khilafat of the Promised Messiah has only existed for 48 years and many cats are dreaming of the meat they can feed on, and are planning to destroy the khilafat.”
“So I give glad news to a person whom Allah Ta`ala makes third Khalifa, if he has belief in Allah Ta`ala, then what are Mannan [Abdul Mannan Omar son of Maulana Noor Ud Din], Wahaab [Abdul Wahaab Omar son of Maulana Noor Ud Din], and Paighamis [LAM elders]? And if world governments will oppose him, they will destroyed (Shout Takbeer).”
Page 5 (within 1st para): “I have constituted a committee to consider the Christian way of election … Their way is very simple. A small group from among their leading learned men elects the Pope, and the rest of the Christian world accepts it.”
“At this time Shaitan has chosen the sons of Hazrat Khalifa 1, just as at the time of Adam he chose the tree of life …” (p. 5). On the same page he says that the sons of Khalifa 1, and their sons also, are expelled from the Jamaat.
“Therefore, on the pattern of the Islamic procedure, which I shall set down later, for the future in regard to the election of the Khalifa, I abrogate the provision that the election would be done by the Shura, and lay down, instead, that in future whenever the time comes for a new Khalifa to be elected, the Nazirs and members of the Sadr Anjuman Ahmadiyya; the Vokala of the Tehrik-i-Jadid; the living members of the House of the Promised Messiah: (at the time of revision, under suggestion from some friends) the Sahaba of the Promised Messiah, to whom certificates of Sahabiat would be issued by the Sadr Anjuman, after due inquiry; Principal of the Jamiatul Mobashirin; Principal of Jami’a Ahmadiyya; the Mufti of the Ahmadiyya Movement; the Amirs of the Local Jama’ats in Sindh and the Punjab; and the Amir of the Jama’at in East Pakistan, would carry out the Election.”
“Similarly, (when revising this document) I add: those who have twice been elected as Amir of some local Jama’at, at the time of an election, though they may not happen to be Amir of any local Jama’at : those who may have served in some foreign mission for a period of at least one year, free of any blot in the eyes of the Centre (List of such missionaries to be maintained and publisbed by Tahrik-i-Jadid; missionaries who have worked for at least one year as Raisut-Tabligh for any district or provincel; List to be the responsibility of the Sadr Anjuman Ahmadiyya) provided they arrive in time. Secretary of the Shura would flash the news all over the country. After this, those who fail to reach, would fail to their own disadvantage, the procedure not to be held up, to wait for them.” (Khilafat-i-Haqqa, published by Al-Shirkatul Islamia, Ltd., Rabwah, page 15, 16)
“Tarikh-e-Ahmadiyyat” Vol 19 for further details.