The Data Migration is an OVA that tells the events after the end of the anime. It includes the, missing material from the end of the manga, as well as more complete information, of the events in Future Diary Redial centered around Yuno's 3rd incarnation.
Summary
Muru Muru is imprisoned by her 3rd incarnation but not before absorbing the memories left of the dying Yuno.
Due to the changes in the future, Yuno's family is now a normal and happy family, and Yuno is a normal teenager herself. Kurusu's son was spared of death due to Minene Uryu's intervention while being happily married to Nishijima.
While everything seems to be nice, Yuno start to have flashes of memory regarding a certain person that she cannot remember, but she feels that person is important and thus is sad.
The intervention on the future has made Deus Ex Machina forsake the Survival Game as told by John Bacchus as the game would have not brought a successor that would keep the world going. Instead Bacchus attempts to create several new games, but is completelly rejected and expelled by Muru Muru who is bored of seeing games in which Bacchus gets an unfair advantage.
Deus asks Uryu to be the next God in the third world , but as it was shown before she is lucky with the live she's got, and that they were "two other problems", holding her back from beeing the new god, and Deus then desists.
Yuno is seen talking with an unknown individual regarding the memories that have been haunting her, but gets no definitive answers, save that the person she remembers is indeed important to her.
Muru Muru detects an anomaly in the space-time-continuum. But neither she nor Deus can understand the cause.
Yuno is friends with Hinata, Mao, Ouji Kosaka and Akise Aru and they spend a fun time in the beach. Akise Aru is secretly an observer sent to keep a close eye on Yuno and on other possible anomalies that may occur. Yomotsu Hirasaka is still a vigilante on night while a shop owner in day selling merchandise of his vigilante self. His shop is visited by Yuno and the others, and finds much to his chargrin that his vigilante self is considered a freak.
Ai Mikami and Orin Miyashiro work for Tsubaki Kasugano and attempt to secure Akise as per her request as she has romantic feelings for him. Things take a turn for the worse however when they confuse Akise for Ouji, as Tsubaki hugs him and realizes the truth, she screams in terror prompting Ouji to escape.
Eventually, Yuno begins to feel each time more and more worried about the recurring memories, and talks with the mysterious person more often. Eventually Yuno reaches the alternate dimension of Deus and begins to search for clues. Muru Muru discovers her and uses pilots a giant mecha in order to prevent her intrusion. However Minene appears to back up Yuno and tells her to send her greets to the "him".
Yuno goes on her way but is interrumpted by Akise on the way. Akise claims he won't let Yuno go, because she and her other incarnations have been a problem for him (as well as his own personal feelings for Yuki) and won't let Yuno meet "him". Yuno refuses to retreat as she wants to know the truth and so he attacks her with a sword. The two briefly engage each other briefly with Akise eventually having Yuno at her mercy and attempts to kill her. However Yuno manages to pin Akise down and claims she does not care about his feelings and that she will meet the person that has been calling her. Akise asks Yuno too , if she could send his greets to "him".
Yuno goes on and she find a big spheric room similar to the one Yuki was imprisoned by Yuno beforehand. Muru Muru attempts to stop Yuno but Deus stops her trying to see if she can change the future. Yuno meets the first incarnation of Muru Muru who is revealed to be the person trying to contact her. It is revealed by Deus that as Muru Muru absorbed the feelings and memories of her first incarnation for years, these have been affecting Muru Muru causing her to contact Yuno in order to give them back to her, Muru Muru succeeds in passing her them into Yuno through the fragment of Deus.
Yuno then proceedes to smash the spheric room, which opens a rift with the second world, causing her and Yuki to finally meet.