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How to prove that if $a,b,c,d$ and $a',b',c',d'$ are 2 quadruples of distinct points in extended complex plane, and if the cross ratios of these quadruples are equal then there exists Möbius transformation $M$ such that $M(a)=a', M(b)=b',M(c)=c',M(d)=d'$

I am reading a paper and there is already proof that if there exists then the cross ratio is preserved but the remaining is left as an exercise.Any hint would be appreciated.

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