He doesn't get it back but he asks Katniss a series of questions that fill him in. It's as if he's back to normal, but I wish that he could get his original memory back to normal.
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The Rebels decide to rescue Peeta in Mockingjay because without Peeta they won't have Katniss's help. Katniss is severely depressed with him in the Capitol's hands and she can't think straight while Peeta is with them. That is the only reason why they rescued Peeta. Not because they care about him. They only cared about Katniss because she is the Mockingjay.
Yes, the Rebels rescue Peeta, and Katniss is overjoyed to see him. But when Katniss enters Peeta's hospital room Peeta tries to choke her almost killing her. The rebels soon realized he was hijacked (his memories were altered with tracker jacker venom) but eventually he becomes normal again and he and Katniss get married and have children.
She is someone who is familiar to Peeta through his childhood memories from District 12.
They do it throughout the book, at random times.
Katniss Everdeen ends up with Peeta Mellark. It states what in the last book Mockiingjay in the epilogue and last paragraph before the epilogue. They end up marrying and having two children. you should read it.