In last week's post, Karjakin's/Carlsen's Olympiad Records, I noted
Karjakin has played three times for the Ukraine and three times for Russia.
The corresponding Olimpbase charts show that the change of federation took place between the 2008 and 2010 Olympiads. Wikipedia's page, Sergey Karjakin, confirms,
Personal life: On July 25, 2009, by the decree of the President of Russia Dmitry Medvedev, Karjakin adopted Russian citizenship. Later that year he transferred chess federations from Ukraine to Russia, in order to get sponsorship and better coaching. He lives in Moscow since 2009. [...] Karjakin considers himself Russian rather than Ukrainian, and supports the 2014 Russian annexation of Crimea (from Ukraine) and Vladimir Putin.
The sequence of events is documented in a series of reports by Chessdom.com. The first report was Karjakin to play for Russia by [Ukrainian] GM Mikhail Golubev for Chess Today (16 April 2009):-
Yesterday Yury Vasilyev included in his ChessPro report from Nalchik the unofficial news that Sergey Karjakin will play for Russia in the near future. Afterwards I spoke with Sergey's father Alexander who confirmed that it is not a secret, and such transfer is their intention. Alexander said that they have nothing against Ukraine, and they are grateful to everyone who helped them in the past.
The story continued the next day with Sergey Karjakin moves to Moscow, changes to Russia Chess Federation (17 April 2009):-
GM Dmitry Komarov spoke with Sergey’s father Alexander Karjakin. "Our family has filed documents to obtain Russian citizenship" – Alexander Karjakin confirmed for newspaper Fakti – "This was Sergey’s solution. We do not have any issues with Ukraine. Here we did everything possible, but unfortunately it is not enough for Sergey to fulfill his dream and become a world champion."
The year 2009 was Karjakin's year of big changes. A few months later, Sergey Karjakin and Kateryna Dolzhikova get married (26 July 2009):-
Karjakin and Dolzhikova become one of the strongest chess couples The 19 years old Ukrainian grandmaster Sergey Karjakin married the 20 years old WGM Kateryna Dolzhikova
At nearly the same time it was confirmed that Sergey Karjakin takes Russian citizenship (1 August 2009):-
At the beginning of 2009 Karjakin decided to move to Russia and join the Russian Chess Federation. A few months later he filed the documents for the federation change. The official decision is a fact, Sergey Karjakin is now player and citizen of Russia. The document was signed on July 25th personally by the Russian President Dmitry Medvedev.
As for the marriage, later that month the newlyweds gave interviews during the Jermuk leg of the 2008-2009 Grand Prix: Interview with WIM Katya Dolzhikova and with GM Sergey Karjakin. Dolzhikova's older sister, Olga, a WGM herself, lives in and plays for Norway. For more about her, see another Chessdom.com article WGM Olga Dolzhikova: Magnus will win the match easily (November 2013). Karjakin's marriage to Katya ended in divorce a few years later. That same Personal life section of Karjakin's Wikipedia page informs,
Karjakin married Galiya Kamalova in May 2014, and a son was born in late 2015. He was previously married to Ukrainian Woman Grandmaster [WIM?] Kateryna Dolzhikova.
Given the ongoing strife between the Ukraine and Russia, Karjakin's transfer from the Ukraine to Russia is not viewed favorably by the Western media. I once wrote a post on Ukrainian Chess Players, and know that the political realities of the region are difficult to fathom. The real world is not reducible to black and white, nor to good and evil.