For some collectors, mail from or to Russian Alaska is a Holy Grail. Back in 1960, Tchilingirian and Stephen devoted two pages to "Russian America" in Part Six of their Stamps of the Russian Empire Used Abroad. At the end of their two pages, they write "no material known so far"(page 496).
Nowadays, the Internet makes it easy to establish that letters from Russian Alaska exist, notably in museums and archives in Finland, since Finns were very active among the sailors, traders and adventurers who made their way to Alaska. But I do not know if anyone has studied the letters for postal markings - if the letters were entire letters then they would be addressed and probably show some markings. The letters are referred to in historical studies of the colonisation of Alaska.
However, a new development has now occurred. An 1851 entire letter from Alaska to Finland has appeared in auction, and was sold by the Swedish firm Philea on 10 April 2016 for 15 500 euro hammer ( on 3000 euro Starting Price). The letter is undoubtedly genuine and here it is: