One of the requirements one must meet to obtain an indulgence is to pray for the intentions of the pope. When there's no pope, what's the substitute? I guess it's the conclave and the next pope, but I don't know the exact rules on this.
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It's not a prayer for the Pope; it's a prayer for the intention of the Pope.
Although certain functions of the Papacy are carried out during a vacancy under the Cardinal Camerlengo, there is no "Sovereign Pontiff".
Given that a prayer for the intention of the Sovereign Pontiff cannot be properly fulfilled in a vacancy, it would appear that any indulgence will be partial only.
Each year, the Vatican announces the Pope's Intentions for the year ahead (see e.g. http://www.ewtn.com/faith/papalprayer.htm ) - so by praying for the intentions the last Supreme Pontiff indicated for that month, surely you are praying for the Pope's Intentions, even when there is no current Pope?
I made some research myself, and I found that someone tried hard to learn after death of John Paul II. Here is an English translation of a latin answer from the office of Apostolic Penitentiary, answering our question:
The answer is awesome: Communion of Saints! It's the pope's job to pray for the Church (and while we pray for the intention of the Sovereign Pontiff, we support mainly this kind of prayers). If he does it while living as a member of ecclesia militans, he will certainly continue in heaven or purgatory.