Update: at this time the alihan777 account appears to have been completely removed from Instagram, perhaps due to growing visibility. Since the photographs used in this post were embedded (for copyright reasons), they are sadly also gone. A good number of them can be found here  [ru] and by following some of the internal links in this post.
It's hard to tell who noticed alihan777 ‘s Instagram account first. Russian TV personality Tina Kandelaki mentioned the nickname in a friendly tweet  [ru] on January 8, 2013, but gave no indication of the owner's identity.
From the start, however, it was obvious that the anonymous album was being updated by either Chechen President Ramzan Kadyrov himself, his press secretary, or someone equally close. The surprisingly candid photographs are all almost exclusively of Kadyrov (seen above dressed in some form of traditional armor).
Some of the photos are surreal. For example, Kadyrov, who is often accused of human rights violations and authoritarianism, can be seen unironically dressed as a Central Asian khan, complete with baby tiger. Nevertheless, RuNet didn't pick up on the story until a week later, when after a few [ru] tweets [ru] it was noticed by St. Petersburg-based culture blogger Corpuscula, who reposted some of the photographs on January 15, and wondered who it was that made them  [ru].
The next day, Marina Litvinovich, a human rights activist and former PR guru, also blogged about the account, bringing it further notoriety. Litvinovich rather mockingly singled out several photographs in which Ramzan Kadyrov is seen enjoying the Chechen countryside along with Vladislav Surkov and Surkov's wife.
Surkov, who is ethnically Chechen, is widely considered to have been the chief ideologue of the Putin presidency. After the 2011 parliamentary elections he was shunted from the President's Administration to a minor ministerial portfolio, which some viewed as a demotion. Following a brief stint as the First Deputy Prime Minister, Surkov now heads the Government Apparatus, the bureaucratic structure charged with supporting the Russian Government (i.e. the Ministries) — a position previously held by Moscow Mayor Sergey Sobyanin.
Perhaps as the result of increased attention the account was briefly made private  [ru], but later came back. Maybe Kadyrov was at first uncomfortable — after all he is a latecomer to the micro-blogging arena, having only started a Twitter account during the summer of 2012 (his first tweet as @RKadyrov  [ru] was on June 20). Until then, bloggers were sometimes fooled by @kadirovrussia  [ru], a humorously fake account active from 2011. While Kadyrov's tweets are mostly boring official announcements, the alihan777 Instagram (started in November, 2012) more than makes up for it.
Does Kadyrov use the account himself? Even when linking to a photograph of himself, Surkov, and Prime Minister Medvedev on his Twitter, Kadyrov remains somewhat tongue in cheek  [ru]:
Вот такую фотку нашел у
@alihan777 instagram.com/p/VMjbDKr5_K/ 
Look at the photo I found at
@alihan777 instagram.com/p/VMjbDKr5_K/ 
However, even though Kadyrov has not publicly acknowledged that he is alihan777, it is almost certainly him. That is, if we are to believe Tina Kandelaki, who [ru] has [ru] been [ru] plugging [ru] alihan777 ever since returning from a recent visit to Chechnya. Tellingly, in her own Instagram photos along with Kadyrov (seen above), she refers [ru] to him as alihan777:
@alihan777 считает, что сейчас правильно инвестировать в бонды и технологии. Очень ему нравится кейс Инстаграма, но считает, что покупать рано
@alihan777 thinks that now is the time to invest into bonds and technology. He really likes the Instagram case, but he thinks that its still too early to buy
Kadyrov, who has spent much of his time as leader of Chechnya solidifying the peace process started by his father Ahmat, often presents a rough exterior in the photos. In that, he seems to follow in the footsteps of his mentor, Vladimir Putin. At other times he exhibits his religiosity. For example, the first photograph in alihan777's album is of a lock of hair allegedly belonging to the Prophet Mohammed  [ru], exhibited in Abu Dhabi. Besides for his religion and tracking down Wahhabi guerrillas in the Chechen mountains, Kadyrov seems to like, in no particular order:
And aging movie stars.
Find more here  [ru].