Of course yes. consider our claim is wrong so we have a group containing $A,B,C,D$ which none of them are friend with everyone. for example $A$ is not friend with $N$ and $B$ is not friend with $M$.then we have two case: case1: $N$ and $M$ are distinct so if we put $N,M,A,B$ in one group then there isn't anyone who is a friend of three others => contradiction case2: all of these four people aren't friend with exactly one person like $N$ now put $N,A,B,C$ in one group same as above it gives us a contradiction So our first claim is true