The Monster group $M$ is the largest sporadic simple group. It is also the group of automorphisms of $196, 884$-dimensional Fischer-Norton-Griess algebra $V_M$. In 2009, A. A. Ivanov offered an axiomatic approach to studying the structure of $V_M$ by introducing the notions of Majorana algebra and Majorana representation. Later, the theory developed, and Majorana representations of several groups were constructed. Our talk is dedicated to the existence of standard Majorana representations of 3-transposition groups for the Fischer list. The main result is that the groups from the Fischer list which admit a standard Majorana representation can be embedded into the Monster group.