Prove that if $n + 1 | n! + 1$ then $n+1$ is a prime number

How can we prove that if : $n+1|n!+1$ then $n$ is a prime number.
My try:
I try to do contrapositive: If $n$ is composite then $n+1 nmid n!+1$ and then to get that if $n$ is composite so $n+1=ab$ when $2 le a le n $ so that $a|n+1$ but here I don’t have idea how to continue, is this the good way?