Integer whose Digits when Grouped in 3s add to 999 is Divisible by 999

Theorem

Let $n$ be an integer which has at least $3$ digits when expressed in decimal notation.

Let the digits of $n$ be divided into groups of $3$, counting from the right, and those groups added.

Then the result is equal to $999$ if and only if $n$ is divisible by $999$.