Verdict
It is not in Fyodor Dostoevsky's work
It is constantly attributed to Dostoevsky and to The House of the Dead, but the sentence is not found in that book or elsewhere in his published writings; its exact origin has not been established.
What they did say
Verified words of Fyodor Dostoevsky
«Man is a mystery. It must be solved, and if you spend your whole life solving it, do not say you have wasted your time; I occupy myself with this mystery because I want to be a man.»
Carta a su hermano Mijaíl, 16 de agosto de 1839 (Собрание сочинений в 15 томах, t. 15, carta n.º 10). Tenía diecisiete años.
«Life is a gift, life is happiness; every minute might have been an age of happiness.»
Carta a su hermano Mijaíl escrita en la fortaleza de Pedro y Pablo, 22 de diciembre de 1849, horas después del simulacro de ejecución (t. 15, carta n.º 37).
«Brother! I have not lost heart or fallen in spirit. Life is life everywhere; life is in ourselves and not in what is outside.»
Misma carta del 22 de diciembre de 1849 (t. 15, carta n.º 37).
