I found Alexei’s diary entry for October 4, 1916 in a fabulous Russian book : «Tsesarevich» (published in Moscow 1998 ). See this thread for more on the book and Alexei’s diaries:
http://hydrogen.pallasweb.com/cgi-bin/yabb/YaBB.cgi?board=alexei;action=display;num=1106495614His diary entries for January 1, until December 24, 1916 are in the book. To my knowledge, these haven’t yet been translated into English.
As for the photo posted by Otmanfan, compared with the other one (with OTMA) and film, it seems you are right…:-/  I had seen the same photo in Grand Duchess George’s (Maria Georgievna) memoirs with an inscription in Russian «Mogilev 1916» (supposedly from her private photo albums) and didn’t pay more attention to it. But I should have noticed that Alexei isn’t even wearing the same uniform than on the group photo (and film)
… shame on me!
. On the « Otmafan » photo, Nicholas II and Alexei are wearing the Konvoi’s everyday uniform (dark blue tunic, red shirt, AND gold & silver braid). But on the group photo, they are wearing the field uniform WITHOUT braid… and Alexei does indeed seem to be slightly taller than on the other photo. Another clue - hard to tell, due to photo angle - but he  doesn’t seem to have his St. George’s medal (he got it on October 25, 1915). If so, there’s only one possibility : the «Otmanfan» photo was taken one year earlier, on October 4, 1915. Unfortunately, Alexei hadn’t yet begun writing his diary. But I checked his father’s : they had arrived at Headquarters the day before (it was Alexei’s first stay there). On October 4, 1915, the Tsar writes that there was a Prayer Service and Parade of the Cossack Escort on the small square (in front of the Headquarters). He doesn’t mention Alexis, but I believe he would have attended the parade, as he had done many times before.
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Grand Duchess George’s memory must have failed her (maybe she added the caption years later). All this shows that it’s often quite difficult to identify and date Romanov photos properly, and that a great deal of research and detective work has to be done sometimes. You would have done an excellent sleuth AlexisLVR!
