The Gemara in Sukkah on daf מא עמוד ב' relates a story of Rabban Gamliel, Rabbi Yehoshua, Rabbi Elazar ben Azaria, and Rabbi Akiva riding on a boat. The time came to shake lulav, but only Rabban Gamliel had a lulav. Since it is required to shake one's own lulav on the first day of Sukkot, Rabban Gamilel gave his lulav as a gift to Rabbi Yehoshua. After being yotzei, Rabbi Yehoshua gave the lulav as a gift to Rabbi Elazar ben Azaria who gave it as a gift to Rabbi Akiva who subsequently returned it as a gift back to Rabban Gamliel.
The Gemara explains that the reason it was required to say in the story that Rabbi Akiva returned the lulav to Rabban Gamliel was to teach that a gift given on the condition that it will be re-gifted back to the original owner is considered a gift.
Further down on the page, we also learn that if someone gives a lulav as a gift on the condition that it will be returned, and the person does not return it, the receiver is not yotzei the mitzvah of lulav because he used a stolen lulav.
Tosfot explains that Rabban Gamliel actually gave the lulav on condition that it would be returned after all of the others on the boat had been yotzei.
So my question is as follows: What if Rabbi Akiva had decided to keep the lulav at the end and not return it to Rabban Gamliel? Would Rabbi Yehoshua and Rabbi Elazar ben Azaria be yotzei lulav? They did not personally steal the lulav, so I could definitely believe that if a person steals a gifted lulav, then the retroactiveness of the theft only goes back to when the person acquired the lulav. If others had it before him, since they didn't steal it, they could be yotzei. However, the gift was only given on the condition that it would be returned, which it was not, so perhaps the gift is considered to never have taken effect.